Publications

2026

• Han, Z., Yu, K., & Zuazua, E. (2026). Optimal Decay Rate for a Degenerate Hyperbolic-Parabolic Coupled System. SIAM J. Control Optim., . https://doi.org/10.1137/25M1776184, FAU CRIS
• Jin, S., Ma, C., & Zuazua, E. (2026). Transmutation based Quantum Simulation for Non-unitary Dynamics. SIAM J. Sci. Comput.. arXiv: 2601.03616 , FAU CRIS
• Falk, H., Hernandez, M., Leugering, G., Schmidt, M., & Zuazua, E. (2026). Domain Decomposition for Gas Network Control. Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks. Chapter 17. Ed. by A. Martin, F. Liers, F. Hante, J. Lang, M. Pfetsch, C. Tischendorf, and S. Ulbrich. , FAU CRIS
• Sonego, M. & Zuazua, E. (2026). Crossover asymptotics and a sharp confinement rate for the viscous Burgersequation. (Unpublished, Submitted). , FAU CRIS
• Liu, Q., Lü, Q., & Zuazua, E. (2026). Autonomous Flows: Exact Finite Interpolation and Uniform Approximation Obstructions. (Unpublished, Submitted). , FAU CRIS
• Biccari, U., Chen, J., Morales, R., & Zuazua, E. (2026). Bi-HYCO: Bi-Objective Cooperative Learning for PDE Parameter Identification under Fragmented Observations. (Unpublished, Submitted). arXiv: 2609.06511 , FAU CRIS
• Zuazua, E. (2026). Good Solutions, Bad Coordinates: The Coercivity Gap in Neural Partial Differential Equation Solvers. SIAM News, 59(7). arXiv: 2510.03303 , FAU CRIS
• Biccari, U., Chen, J., Morales, R., & Zuazua, E. (2026). Bi-HYCO: Bi-Objective Cooperative Learning for PDE Parameter Identification under Fragmented Observations. (Unpublished, Submitted). arXiv: 2609.06511 , FAU CRIS
• Zamorano Aliaga, S. & Zuazua, E. (2026). Tracking controllability for finite-dimensional linear systems. (Unpublished, Submitted). arXiv: 2407.18641 , FAU CRIS
• Zuazua, E. (2026). Machine Learning and Control: Foundations, Advances, and Perspectives. Proceedings of the International Congress of Mathematicians 2026. SIAM. International Mathematical Union, 7, 267-286. arXiv: 2510.03303 , FAU CRIS
• Liverani, L. & Zuazua, E. (2026). HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling. arXiv preprint. arXiv: 2509.14123 , FAU CRIS
• Biccari, U., Huang, Q., & Zuazua, E. (2026). Interior interpretability with attention rollout: contraction and propagation profiles in Transformers. arXiv preprint. arXiv: 2607.22367 , FAU CRIS
• Bellomo, N., Brezzi, F., & Zuazua, E. (2026). New trends in mathematics for scientific machine learning. Math. Models Methods Appl. Sci., 36 (8), 1615-1621. https://doi.org/10.1142/S0218202526020033 , FAU CRIS
• Ignat, L. & Zuazua, E. (2026). Sharp Numerical Approximation of the Hardy Constant. Discrete and Continuous Dynamical Systems (DCDS), 54, 15-32. https://doi.org/10.3934/dcds.2025165 arXiv: 2506.11809 , FAU CRIS
• Liu, K., Wang, Z., & Zuazua, E. (2026). Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning. Physica D: Nonlinear Phenomena, 483. https://doi.org/10.1016/j.physd.2026.135288 , FAU CRIS
• Lopez-Montero, D., Liverani, L., Zuazua, E., & Kobeleva, X. (2026). Hybrid Modeling of Whole-Brain Dynamics balances Data Fidelity and Interpretability. (Unpublished, Submitted). , FAU CRIS
• Alvarez-Lopez, A., Liverani, L., & Zuazua, E. (2026). Constructive interpolation and generalization rates for Neural ODEs: a control perspective. (Unpublished, Submitted). , FAU CRIS
• Alcalde, A., Ji, Z., & Zuazua, E. (2026). Reachability and asymptotics of Gaussian Transformer dynamics. (Unpublished, Submitted). , FAU CRIS
• Ignat, L. I. & Zuazua, E. (2026). Optimal convergence rates for the finite element approximation of the Sobolev constant. Found. Comput. Math.. arXiv: 2504.09637 , FAU CRIS
• Li, Y., Xiaoyang, W., & Zuazua, E. (2026). Fully Discrete High-Order DG Scheme for Waves: Dispersion and Observability. (Unpublished, Submitted). arXiv: 2605.17464 , FAU CRIS
• Liu, K. & Zuazua, E. (2026). Geometric Asymptotics of Score Mixing and Guidance in Diffusion Models. (Unpublished, Submitted). arXiv: 2605.12231 , FAU CRIS
• Alcalde, A., Fantuzzi, G., & Zuazua, E. (2026). Exact Sequence Classification with Hardmax Transformers. Math. Found. Mach. Learn., 2(2). https://doi.org/doi.org/10.1007/s44439-026-00005-y arXiv: 2502.02270 , FAU CRIS
• Song, Y. W. Z. & Zuazua, E. (2026). Approximate and Weighted Data Reconstruction Attack in Federated Learning. IEEE Trans. Big Data. arXiv: 2308.06822 , FAU CRIS
• Ibañez de Opakua, A., Bizkarguenaga, M., de Diego, Á., Conde, R., González-Valle, B., Gil-Redondo, R., Santana, T., Seco, M. L., Cenarro, A., Lope, V., Margarita, S., Pelusi, S., Habisch, H., Haudum, C., Verheyen, N., Obermayer-Pietsch, B., Sorando-Fernandez, M. P., Arana-Arri, E., Meijide, S., Salazar, A. M., Hernandez, G., Baldán-Martín, M., Martínez-González, P. J., Suárez-Trujillo, F., Audije-Gil, J., Arriaga, J. I., Iriberri, M., Moran, M. Á., Camino, X., Gracia, A., Bernardo-Seisdedos, G., Sousa, A., Oliveira, N., Verde, I., Zaro Bastanzuri, M. J., González Fernández, M. R., Fernández-Bergés, D., Navarrete-Arias, L., Llamas-Velasco, M., Biccari, U., Morales, R., Madl, T., Unda-Urzaiz, M., Carracedo, A., Diercks, T., Castelló, A., Schäfer, H., Spraul, M., Cannet, C., Tasic, L., Sanchez-Pernaute, R., Buguianessi, E., Anstee, Q., Embade, N., Lu, S. C., Mera, F., Valenti, L., Luchinat, C., Cibrián, D., de la Fuente, H., Civeira, F., Arenas, D., Gisbert, J. P., Chaparro, M., Giskeodegard, G., Bathen, T., Zuazua, E., Mato, J. M., & Millet, O. (2026). Mapping metabolic aging and disease-associated acceleration using an interpretable NMR-based clock. (Unpublished, Submitted). , FAU CRIS
• Li, Z. & Zuazua, E. (2026). Hamiltonian Interface Dynamics for Reduced-Order Optimization of Incompressible Mixing. arXiv preprint. arXiv: 2605.04688 , FAU CRIS
• Ftouhi, I. & Zuazua, E. (2026). Sensor Placement via Large Deviations in the Eikonal Equation. Arab. J. Math. https://doi.org/10.1007/s40065-026-00628-1, arXiv: 2508.21469 , FAU CRIS
• Lyu, K., Biccari, U., Wang J. (2026). Operator learning for prescribed-time stabilization of reaction-diffusion systems. arXiv preprint. arXiv: 2602.23157
• Chen, J., Biccari, U., & Wang, J. (2026). Learning the Riccati solution operator for time-varying LQR via Deep Operator Networks. arXiv preprint. arXiv: 2604.18507
• Biccari, U., Ibanez-de-Opakua, A., Mato, J. M., Millet, O., Roberto, M., & Zuazua, E. (2026). Fair feature attribution for multi-output prediction: a Shapley-based perspective. arXiv preprint. arXiv: 2602.22882 , FAU CRIS
• Liverani, L. & Zuazua, E. (2026). HYCO: A formalism for Hybrid-Cooperative PDE modelling. (Unpublished, Submitted). , FAU CRIS
• Li, Z., Liu, K., Liverani, L., & Zuazua, E. (2026). Universal Approximation of Dynamical Systems by Semiautonomous Neural ODEs and Applications. SIAM J. Numer. Anal., 64(1), 193-223. https://doi.org/10.1137/24M1679690 arXiv: 2407.17092 , FAU CRIS
• Sonego, M. & Zuazua, E. (2026). Control of a Lotka-Volterra System with Weak Competition. Communications in Information and Systems (CIS), 26, 27-62. arXiv: 2409.20279 , FAU CRIS
• Hu, W., Li, Z., Liu, K., Zhang, Y., & Zuazua, E. (2026). A Structure-Preserving Numerical Scheme for Optimal Control and Design of Mixing in Incompressible Flows. (Unpublished, Submitted). arXiv: 2601.06294
• Li, Z., Liu, K., Song, Y., Yue, H., & Zuazua, E. (2026). Deep Neural ODE Operator Networks for PDEs. M3AS, arXiv: 2510.15651
• Brull, A., Aguti, S., Bolduc, V., Hu, Y., Jimenez-Gutierrez, D. M., Zuazua, E., Del-Rio, J. S. O., Zhou, H., Muntoni, F., G. Bönnemann, C., & Uribe-Etxebarria, X. (2026). Training Together, Diagnosing Better: Federated Learning for Collagen VI-Related Dystrophies. (Unpublished, Submitted). arXiv: 2512.16876
• Liu, K. & Zuazua, E. (2026). Moments, Time-Inversion and Source Identification for the Heat Equation. Inverse Probl.. arXiv: 2507.02677 , FAU CRIS
• Zuazua, E. (2026). Machine Learning and Control: Foundations, Advances, and Perspectives. arXiv preprint. arXiv: 2510.03303 , FAU CRIS
• Liu, K., Wang, Z., & Zuazua, E. (2026). A Potential Game Perspective in Federated Learning. (Unpublished, Submitted). , FAU CRIS
• Lü, Q., Ma, B., & Zuazua, E. (2026). Mean-Square Stability of Continuous-Time Stochastic Model Predictive Control. (Unpublished, Submitted). , FAU CRIS
• Morales, R., Santos, M. C., & Carreño, N. (2026). Insensitizing the tangential gradient for reaction–diffusion equations with dynamic boundary conditions. Journal of Optimization Theory and Applications, 208(1), 55.
• Chen, J., Wang, J., & Yu, X. (2026). Adaptive output tracking for 1-D unstable heat equations with unknown multi-frequency exosystem. Commun. Nonlinear Sci. Numer., 152, 109–142. https://doi.org/10.1016/j.cnsns.2025.109142
• Anđjelić, M., da Fonseca, C. M., & Stanić, Z. (2026). An equitable partition based construction of graphs with the same spectral radius. Appl. Math. Comput., 510, 6. https://doi.org/10.1016/j.amc.2025.129696
• da Fonseca, C. M. (2026). A comment on the spectrum of a four-parameter extension of the Sylvester-Kac matrix. J. Comput. Appl. Math., 472, 3. https://doi.org/10.1016/j.cam.2025.116786

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2025

• Liu, K. & Zuazua, E. (2025). A PDE perspective on generative diffusion models. (Unpublished, Submitted). , FAU CRIS
• Dehman, B., Ervedoza, S., & Zuazua, E. (2025). Regional and Partial Observability and Control of Waves. Special issue on the memory of H. Brezis. C. R. Acad. Sci. Paris. arXiv: 2504.18976 , FAU CRIS
• Song, Y., Wang, Z., & Zuazua, E. (2025). FedADMM-InSa: An inexact and self-adaptive ADMM for federated learning. Neural Networks, 181, 106–772. https://doi.org/10.1016/j.neunet.2024.106772 , FAU CRIS
• Fernandes Barreira, J., Sonego, M., & Zuazua, E. (2025). Boundary and Interior Control in a Diffusive Lotka-Volterra Model. (Unpublished, Submitted). , FAU CRIS
• Acero, A., Jimenez-Rodriguez, D. M., Pighin, D., Zuazua, E., Del Rio, J., & Uribe-Etxebarria, X. (2025). The Sherpa.ai Blind Vertical Federated Learning Paradigm to Minimize the Number of Communications. arXiv preprint. arXiv: 2510.17901 , FAU CRIS
• Floridia, G. & Zuazua, E. (2025). Analysis and Numerics of Design, Control and Inverse Problems. Springer Nature Singapore. https://doi.org/10.1007/978-981-96-6182-4
• Alcalde, A., Fantuzzi, G., & Zuazua, E. (2025). Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis. SIAM J. Math. Data Sci., 7(3), 1367–1393. https://doi.org/10.1137/24M167086X arXiv: 2407.01602
• Dehman, B. & Zuazua, E. (2025). Boundary Sidewise Observability of the Wave Equation. Journal of the European Mathematical Society (JEMS). https://doi.org/10.4171/jems/1688 arXiv: 2310.19456
• Trélat, E. & Zuazua, E. (2025). Turnpike in Optimal Control and Beyond: A Survey. Modeling and Optimization in Space Engineering, Challenges of the Near Future. arXiv: 2503.20342
• Affili, E. & Zuazua, E. (2025). Controllability of diffusive Lotka–Volterra strongly competitive systems under boundary constrained controls. arXiv preprint. arXiv: 2508.00713
• Hernández, M. & Zuazua, E. (2025). Random Batch Methods for Discretized PDEs on Graphs. arXiv preprint. arXiv: 2506.11809
• Liu, K. & Zuazua, E. (2025). Moments, Time-Inversion and Source Identification for the Heat Equation. arXiv preprint.
• Hernández, M. & Zuazua, E. (2025). Constructive Universal Approximation and Finite Sample Memorization by Narrow Deep ReLU Networks. arXiv preprint.
• Fattah, Z., Ftouhi, I., & Zuazua, E. (2025). Optimal \(L^p\)-approximation of convex sets by convex subsets. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods, 261, 18. https://doi.org/10.1016/j.na.2025.113866
• Crin-Barat, T., Shou, L., & Zuazua, E. (2025). Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped \(p\)-system. Ann. Inst. Henri Poincaré C, Anal. Non Linéaire, 42(5), 1165–1218. https://doi.org/10.4171/AIHPC/128
• Álvarez-López, A., Orive-Illera, R., & Zuazua, E. (2025). Cluster-based classification with neural odes via control. J. Mach. Learn., 4(2), 128–156. https://doi.org/10.4208/jml.241114
• De Nitti, N., Serre, D., & Zuazua, E. (2025). Pointwise constraints for scalar conservation laws with positive wave velocity. Z. Angew. Math. Phys., 76(3), 17. https://doi.org/10.1007/s00033-025-02459-0
• Crin-Barat, T., Liverani, L., Shou, L., & Zuazua, E. (2025). Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: an algorithmic approach. J. Math. Pures Appl. (9), 202, 103757. https://doi.org/10.1016/j.matpur.2025.103757
• Bárcena-Petisco, J. A. & Zuazua, E. (2025). Tracking controllability for the heat equation. IEEE Trans. Autom. Control, 70(3), 1935–1940. https://doi.org/10.1109/TAC.2024.3476174
• Liu, K. & Zuazua, E. (2025). Representation and regression problems in neural networks: Relaxation, generalization, and numerics. Math. Models Methods Appl. Sci., 35(6), 1471–1521. https://doi.org/10.1142/S0218202525500228 , FAU CRIS
• Bárcena-Petisco, J. A., Cavalcante, M., Coclite, G. M., De Nitti, N., & Zuazua, E. (2025). Control of hyperbolic and parabolic equations on networks and singular limits. Math. Control Relat. Fields, 15(1), 348–389. https://doi.org/10.3934/mcrf.2024015
• Biccari, U. & Zuazua, E. (2025). Gaussian beam ansatz for finite difference wave equations. Found. Comput. Math., 25(1), 1–54. https://doi.org/10.1007/s10208-023-09632-9
• Liu, K. & Zuazua, E. (2025). Moments, Time-Inversion and Source Identification for the Heat Equation. (Unpublished, Submitted). arXiv: 2507.02677
• Biccari, U., Warma, M., & Zuazua, E. (2025). Boundary observation and control for fractional heat and wave equations. (Unpublished, Submitted). arXiv: 2504.17413
• Biccari, U. & Zuazua, E. (2025). Gaussian beam ansatz for finite difference wave equations. Found. Comput. Math., 25(1), 1–54. https://doi.org/10.1007/s10208-023-09632-9
• Biccari, U. (2025). Spiking Neural Networks: a theoretical framework for Universal Approximation and training. (Unpublished, Submitted). arXiv: 2509.21920
• Lyu, K., Biccari, U., & Wang, J. (2025). Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels. (Unpublished, Submitted). arXiv: 2508.03242
• Morales, R. & Biccari, U. (2025). A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints. (Unpublished, Submitted). arXiv: 2507.13983
• Biccari, U., Warma, M., & Zuazua, E. (2025). Boundary observation and control for fractional heat and wave equations. (Unpublished, Submitted). arXiv: 2504.17413
• Aliaga, S. Z. (2025). Book review of: T. L. Molloy et al., Inverse optimal control and inverse noncooperative dynamic game theory. A minimum-principle approach. SIAM Rev., 67(3), 650–651. https://doi.org/10.1137/24M1635120
• Zamorano, S. (2025). Almost periodic turnpike phenomenon for time-dependent systems. Syst. Control Lett., 199, 8. https://doi.org/10.1016/j.sysconle.2025.106069
• García, G., Vidal, J., & Zamorano, S. (2025). A control-based spatial source reconstruction in fractional heat equations. (Unpublished, Submitted). arXiv: 2510.07528
• Morales, R. (2025). SHAP values through general Fourier representations: theory and applications. (Unpublished, Submitted). arXiv: 2511.00185
• Chorfi, S., Hasanov, A., & Morales, R. (2025). Identification of source terms in the Schrödinger equation with dynamic boundary conditions from final data. Z. Angew. Math. Phys., 76(3), 22. https://doi.org/10.1007/s00033-025-02505-x
• Carreño, N., Mercado, A., & Morales, R. (2025). Local null controllability of a cubic Ginzburg-Landau equation with dynamic boundary conditions. J. Evol. Equ., 25(3), 31. https://doi.org/10.1007/s00028-025-01089-3
• Morales, R. & Ramírez-Ganga, J. (2025). Identification of Source Terms in the Ginzburg-Landau Equation from Final Data. (Unpublished, Submitted). arXiv: 2511.07345
• Morales, R. & Biccari, U. (2025). A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints. (Unpublished, Submitted). arXiv: 2507.13983
• Chorfi, S., Maniar, L., & Morales, R. (2025). Controllability and Inverse Problems for Hyperbolic and Dispersive Equations with Dynamic Boundary Conditions. (Unpublished, Submitted). arXiv: 2505.14795
• Carrillo, H., Mercado, A., & Morales, R. (2025). Simultaneous reconstruction of two potentials for a nonconservative Schrödinger equation with dynamic boundary conditions. (Unpublished, Submitted). arXiv: 2502.02758
• Lyu, K., Wang, J., Zhang, Y., & Yu, H. (2025). Neural operators for adaptive control of freeway traffic. Automatica, 182, 112553.
• Lyu, K., Wang, J., & Cao, Y. (2025). Neural operator approximations for boundary stabilization of cascaded parabolic PDEs. International Journal of Adaptive Control and Signal Processing, 39(7), 1503–1520.
• Lyu, K., Biccari, U., & Wang, J. (2025). Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels. arXiv preprint arXiv:2508.03242.
• Lyu, K., Wang, J., Zhang, Y., & Yu, H. (2025). Neural operators for adaptive control of traffic flow models. IFAC-PapersOnLine, 59(8), 13–18.
• Chen, J. & Wang, J. (2025). A kind of observer-based active disturbance rejection control method for the stabilization of a class of Timoshenko beams. EECT, 14(5), 1055–1068. https://doi.org/10.3934/eect.2025025
• Lai, M., Song, Y., Yuan, X., Yue, H., & Zeng, T. (2025). The hard-constraint PINNs for interface optimal control problems. SIAM J. Sci. Comput., 47(3), c601–c629. https://doi.org/10.1137/23M1601249
• Wu, H. & Yuan, X. (2025). Breaking quadrature exactness: A spectral method for the Allen–Cahn equation on spheres. (Unpublished, Submitted). arXiv: 2305.04820
• da Fonseca, C. M. (2025). On the generating functions of products mixing two \(k\)-Fibonacci and other sequences. Georgian Math. J., 32(6), 933–938. https://doi.org/10.1515/gmj-2025-2030
• da Fonseca, C. M., K\iz\ilate\cs, C., & Terzio\uglu, N. (2025). The determinant and a factorization of a Toeplitz matrix with some type of Horadam numbers entries. Log. J. IGPL, 33(6), 13. https://doi.org/10.1093/jigpal/jzae065
• da Fonseca, C. M., K\iz\ilate\cs, C., Saraiva, P., & Shannon, A. G. (2025). Generalised Leonardo numbers. Log. J. IGPL, 33(6), 12. https://doi.org/10.1093/jigpal/jzaf005
• da Fonseca, C. M., Kizilate\cs, C., & Terzio\uglu, N. (2025). The determinants and the inverses of the \(\left(\frac2ak^2+2,a,a\right)\)-\(L_k\)-Toeplitz and the \((2,k^2+2,k^2+2)\)-\(F_k\)-Toeplitz matrices. Log. J. IGPL, 33(6), 17. https://doi.org/10.1093/jigpal/jzaf003
• da Fonseca, C. M., Glasser, M. L., & Kowalenko, V. (2025). New identities involving the univariate Lommel and Bessel functions. Appl. Anal. Discrete Math., 19(2), 348–369. https://doi.org/10.2298/AADM240809015F
• Du, Z. & da Fonseca, C. M. (2025). General Sylvester-Kac matrices with plain eigenvalues. Comput. Appl. Math., 44(8), 19. https://doi.org/10.1007/s40314-025-03352-2
• da Fonseca, C. M., Glasser, M. L., & Kowalenko, V. (2025). Chebyshev polynomials of the first kind and the univariate Lommel function: integral representations. Open Math., 23, 16. https://doi.org/10.1515/math-2024-0113
• Du, Z. & da Fonseca, C. M. (2025). New families of trees determined by their spectra. Linear Algebra Appl., 722, 101–113. https://doi.org/10.1016/j.laa.2025.05.007
• Du, Z. & da Fonseca, C. M. (2025). The real symmetric matrices with a given rank and a \(\mathrmP\)-set with maximum size. Discrete Math., 348(11), 8. https://doi.org/10.1016/j.disc.2025.114572
• Du, Z. & da Fonseca, C. M. (2025). A note on the eigenvalues of a Sylvester-Kac type matrix with off-diagonal biperiodic perturbations. J. Comput. Appl. Math., 461, 6. https://doi.org/10.1016/j.cam.2024.116429

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2024

• Lecaros, R., López-Ríos, J., Montecinos, G. I., & Zuazua, E. (2024). Optimal control approach for moving bottom detection in one-dimensional shallow waters by surface measurements. Math. Methods Appl. Sci., 47(18), 13973–14004. https://doi.org/10.1002/mma.10251
• Veldman, D. W. M., Borkowski, A., & Zuazua, E. (2024). Stability and convergence of a randomized model predictive control strategy. IEEE Trans. Autom. Control, 69(9), 6253–6260. https://doi.org/10.1109/TAC.2024.3375253
• Wang, G., Zhang, Y., & Zuazua, E. (2024). Observability for heat equations with time-dependent analytic memory. Arch. Ration. Mech. Anal., 248(6), 46. https://doi.org/10.1007/s00205-024-02058-9
• Zuazua, E. (2024). Exact controllability and stabilization of the wave equation. Translated from the Spanish by Darlis Bracho Tudares. Cham: Springer. https://doi.org/10.1007/978-3-031-58857-0
• Coclite, G. M., De Nitti, N., Maddalena, F., Orlando, G., & Zuazua, E. (2024). Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings. Math. Models Methods Appl. Sci., 34(8), 1445–1482. https://doi.org/10.1142/S021820252450026X , FAU CRIS
• Lazar, M. & Zuazua, E. (2024). Eigenvalue bounds for the Gramian operator of the heat equation. Automatica, 164, 11. https://doi.org/10.1016/j.automatica.2024.111653
• Della Pietra, F., Fantuzzi, G., Ignat, L. I., Masiello, A. L., Paoli, G., & Zuazua, E. (2024). Finite element approximation of the Hardy constant. J. Convex Anal., 31(2), 497–523.
• Hernández, M. & Zuazua, E. (2024). Uniform turnpike property and singular limits. Acta Appl. Math., 190, 33. https://doi.org/10.1007/s10440-024-00640-7
• Ruiz-Balet, D. & Zuazua, E. (2024). Control of neural transport for normalising flows. J. Math. Pures Appl. (9), 181, 58–90. https://doi.org/10.1016/j.matpur.2023.10.005
• Ruiz-Balet, D. & Zuazua, E. (2024). Pattern control via Diffussion interaction. (Unpublished, Submitted). arXiv: 2407.17514
• Li, Z., Liu, K., Liverani, L., & Zuazua, E. (2024). Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications. (Unpublished, Submitted). arXiv: 2407.17092
• Zuazua, E. (2024). Progress and future directions in machine learning through control theory. (Unpublished, Submitted). , FAU CRIS
• Antil, H., Biccari, U., Ponce, R., Warma, M., & Zamorano, S. (2024). Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation. Evol. Equ. Control Theory, 13(3), 893–924. https://doi.org/10.3934/eect.2024010
• Antil, H., Biccari, U., Ponce, R., Warma, M., & Zamorano, S. (2024). Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation. Evol. Equ. Control Theory, 13(3), 893–924. https://doi.org/10.3934/eect.2024010
• Zamorano, S. & Zuazua, E. (2024). Tracking controllability for finite-dimensional linear systems. (Unpublished, Submitted). arXiv: 2407.18641
• Hernández, M., Lazar, M., & Zamorano, S. (2024). Averaged observations and turnpike phenomenon for parameter-dependent systems. Optimization, 1-24. https://doi.org/10.1080/02331934.2026.2615776, arXiv: 2404.17455
• Fernandez-Cara, E., Morales, R., & Souza, D. A. (2024). Numerical null controllability of parabolic PDEs using Lagrangian methods. (Unpublished, Submitted). arXiv: 2411.14031
• Santos, M. C., Carreño, N., & Morales, R. (2024). An Insensitizing control problem involving tangential gradient terms for a reaction-diffusion equation with dynamic boundary conditions. (Unpublished, Submitted). arXiv: 2407.09882
• Song, Y., Yuan, X., & Yue, H. (2024). The ADMM-PINNs algorithmic framework for nonsmooth PDE-constrained optimization: a deep learning approach. SIAM J. Sci. Comput., 46(6), c659–c687. https://doi.org/10.1137/23M1566935
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• Song, Y., Yuan, X., Yue, H., & Zeng, T. (2024). An Operator Learning Approach to Nonsmooth Optimal Control of Nonlinear PDEs. (Unpublished, Submitted). arXiv: 2409.14417
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• Du, Z. & da Fonseca, C. M. (2024). Sylvester-Kac matrices with quadratic spectra: a comprehensive note. Ramanujan J., 65(3), 1313–1322. https://doi.org/10.1007/s11139-024-00940-4
• da Fonseca, C. M. (2024). The generating function of a bi-periodic Leonardo sequence. Armen. J. Math., 16, 8. https://doi.org/10.52737/18291163-2024.16.07-1-8
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• Anđjelić, M., da Fonseca, C. M., Futorny, V., & Tsylke, A. (2024). Gelfand-Tsetlin modules for Lie algebras of rank $2$. (Unpublished, Submitted). arXiv: 2402.00483

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2023

• Coclite, G. M., De Nitti, N., Keimer, A., Pflug, L., & Zuazua, E. (2023). Long-time convergence of a nonlocal Burgers' equation towards the local \(N\)-wave. Nonlinearity, 36(11), 5998–6019. https://doi.org/10.1088/1361-6544/acf01d
• Biccari, U., Song, Y., Yuan, X., & Zuazua, E. (2023). A two-stage numerical approach for the sparse initial source identification of a diffusion-advection equation. Inverse Probl., 39(9), 30. https://doi.org/10.1088/1361-6420/ace548
• Ruiz-Balet, D. & Zuazua, E. (2023). Neural ODE control for classification, approximation, and transport. SIAM Rev., 65(3), 735–773. https://doi.org/10.1137/21M1411433
• Mazari, I., Ruiz-Balet, D., & Zuazua, E. (2023). Constrained control of gene-flow models. Ann. Inst. Henri Poincaré C, Anal. Non Linéaire, 40(3), 717–766. https://doi.org/10.4171/AIHPC/52
• Lazar, M. & Zuazua, E. (2023). Greedy search of optimal approximate solutions. Pure Appl. Funct. Anal., 8(2), 547–564.
• Ftouhi, I. & Zuazua, E. (2023). Optimal design of sensors via geometric criteria. J. Geom. Anal., 33(8), 29. https://doi.org/10.1007/s12220-023-01301-1
• Ftouhi, I. & Zuazua, E. (2023). Optimal Placement and Shape Design of Sensors via Geometric Criteria. (Unpublished, Submitted).
• Biccari, U. & Zuazua, E. (2023). Multilevel control by duality. Syst. Control Lett., 175, 16. https://doi.org/10.1016/j.sysconle.2023.105502
• Liard, T. & Zuazua, E. (2023). Analysis and numerical solvability of backward-forward conservation laws. SIAM J. Math. Anal., 55(3), 1949–1968. https://doi.org/10.1137/22M1478720
• De Nitti, N. & Zuazua, E. (2023). On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods. Vietnam J. Math., 51(1), 71–88. https://doi.org/10.1007/s10013-022-00598-9
• Esteve-Yagüe, C. & Zuazua, E. (2023). Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods, 227, 18. https://doi.org/10.1016/j.na.2022.113167
• Dehman, B. & Zuazua, E. (2023). Boundary Sidewise Observability of the Wave Equation. (Unpublished, Submitted). arXiv: 2310.19456
• Zuazua, E. (2023). Fourier series and sidewise profile control of 1-d waves. (Unpublished, Submitted). arXiv: 2308.04906
• Abita, R. & Biccari, U. (2023). Multiplicity of solutions for fractional \(q(\cdot)\)-Laplacian equations. J. Elliptic Parabol. Equ., 9(2), 1101–1129. https://doi.org/10.1007/s41808-023-00239-3
• Biccari, U., Song, Y., Yuan, X., & Zuazua, E. (2023). A two-stage numerical approach for the sparse initial source identification of a diffusion-advection equation. Inverse Probl., 39(9), 30. https://doi.org/10.1088/1361-6420/ace548
• Biccari, U. & Zuazua, E. (2023). Multilevel control by duality. Syst. Control Lett., 175, 16. https://doi.org/10.1016/j.sysconle.2023.105502
• Lizama, C. & Zamorano, S. (2023). Boundary controllability for the 1D Moore-Gibson-Thompson equation. Meccanica, 58(6), 1031–1038. https://doi.org/10.1007/s11012-022-01551-3
• Hernández, M., Lecaros, R., & Zamorano, S. (2023). Averaged turnpike property for differential equations with random constant coefficients. Math. Control Relat. Fields, 13(2), 808–832. https://doi.org/10.3934/mcrf.2022016
• Lecaros, R., Morales, R., Pérez, A., & Zamorano, S. (2023). Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions. J. Differ. Equations, 365, 832–881. https://doi.org/10.1016/j.jde.2023.05.014
• Mercado, A. & Morales, R. (2023). Exact controllability for a Schrödinger equation with dynamic boundary conditions. SIAM J. Control Optim., 61(6), 3501–3525. https://doi.org/10.1137/21M1439407
• Lecaros, R., Morales, R., Pérez, A., & Zamorano, S. (2023). Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions. J. Differ. Equations, 365, 832–881. https://doi.org/10.1016/j.jde.2023.05.014
• Zhao, J., Chen, J., & Liu, Z. (2023). Second order evolutionary problems driven by mixed quasi-variational-hemivariational inequalities. Commun. Nonlinear Sci. Numer., 120, 107–192. https://doi.org/10.1016/j.cnsns.2023.107192
• He, B., Xu, S., & Yuan, X. (2023). Extensions of ADMM for separable convex optimization problems with linear equality or inequality constraints. Numerical control. Part B. https://doi.org/10.1016/bs.hna.2022.08.002
• He, B. & Yuan, X. (2023). On construction of splitting contraction algorithms in a prediction-correction framework for separable convex optimization. Commun. Optim. Theory, 2023, 23. https://doi.org/10.23952/cot.2023.28
• Song, Y., Yuan, X., & Yue, H. (2023). A numerical approach to the optimal control of thermally convective flows. J. Comput. Phys., 494, 25. https://doi.org/10.1016/j.jcp.2023.112458
• An, C., Wu, H., & Yuan, X. (2023). Enhanced total variation minimization for stable image reconstruction. Inverse Probl., 39(7), 37. https://doi.org/10.1088/1361-6420/acd4e1
• Liu, Z., Ai, T., Huang, L., Yuan, X., Zhang, M., & Huang, L. (2023). The scattering of seismic waves from saturated river valley with water layer: modelled by indirect boundary element method. Eng. Anal. Bound. Elem., 149, 282–297. https://doi.org/10.1016/j.enganabound.2023.01.021
• He, B., Ma, F., Xu, S., & Yuan, X. (2023). A rank-two relaxed parallel splitting version of the augmented Lagrangian method with step size in \((0, 2)\) for separable convex programming. Math. Comput., 92(342), 1633–1663. https://doi.org/10.1090/mcom/3822
• Ye, J. J., Yuan, X., Zeng, S., & Zhang, J. (2023). Difference of convex algorithms for bilevel programs with applications in hyperparameter selection. Math. Program., 198(2 (B)), 1583–1616. https://doi.org/10.1007/s10107-022-01888-3
• Mordukhovich, B. S., Yuan, X., Zeng, S., & Zhang, J. (2023). A globally convergent proximal Newton-type method in nonsmooth convex optimization. Math. Program., 198(1 (A)), 899–936. https://doi.org/10.1007/s10107-022-01797-5
• Liu, Z., Li, Z., Yuan, X., & Yao, Y. (2023). Convergence Analysis of Randomized SGDA under NC-PL Condition for Stochastic Minimax Optimization Problems. (Unpublished, Submitted). arXiv: 2307.13880
• Anđjelić, M. & Da Fonseca, C. M. (2023). On a determinantal formula for derangement numbers. Kragujevac J. Math., 47(6), 847–850.
• Du, Z. & da Fonseca, C. M. (2023). The determinants of certain double banded \((0,1)\) Toeplitz matrices. Miskolc Math. Notes, 24(3), 1307–1315. https://doi.org/10.18514/MMN.2023.4053
• Du, Z. & da Fonseca, C. M. (2023). The number of P-vertices for acyclic matrices with given nullity. Discrete Math., 346(12), 17. https://doi.org/10.1016/j.disc.2023.113592
• Du, Z. & da Fonseca, C. M. (2023). The characterization of the minimal weighted acyclic graphs. Linear Algebra Appl., 672, 75–92. https://doi.org/10.1016/j.laa.2023.04.019
• Du, Z., da Fonseca, C. M., & Kowalenko, V. (2023). Further developments of basic trigonometric power sums. Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat., RACSAM, 117(3), 17. https://doi.org/10.1007/s13398-023-01442-6
• Alazemi, A., Anđjelić, M., Das, K. C., & da Fonseca, C. M. (2023). Chain graph sequences and Laplacian spectra of chain graphs. Linear Multilinear Algebra, 71(4), 569–585. https://doi.org/10.1080/03081087.2022.2036672
• Anđjelić, M., da Fonseca, C. M., Koledin, T., & Stanić, Z. (2023). An extended eigenvalue-free interval for the eccentricity matrix of threshold graphs. J. Appl. Math. Comput., 69(1), 491–503. https://doi.org/10.1007/s12190-022-01758-3
• da Fonseca, C. M., K\iz\ilate\cs, C., & Terzio\uglu, N. (2023). A second-order difference equation with sign-alternating coefficients. Kuwait J. Sci., 50(2A), 8. https://doi.org/10.48129/kjs.20425
• Du, Z. & da Fonseca, C. M. (2023). Root location for the characteristic polynomial of a Fibonacci type sequence.. Czech. Math. J., 73(1), 189–195. https://doi.org/10.21136/CMJ.2022.0043-22

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2022

• Geshkovski, B. & Zuazua, E. (2022). Optimal actuator design via Brunovsky's normal form. IEEE Trans. Autom. Control, 67(12), 6641–6650. https://doi.org/10.1109/TAC.2022.3181222
• Geshkovski, B. & Zuazua, E. (2022). Turnpike in optimal control of PDEs, ResNets, and beyond. Acta Numerica, 31, 135–263. https://doi.org/10.1017/S0962492922000046
• Esteve, C., Kouhkouh, H., Pighin, D., & Zuazua, E. (2022). The turnpike property and the longtime behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems. Math. Control Signals Syst., 34(4), 819–853. https://doi.org/10.1007/s00498-022-00325-2
• Ruiz-Balet, D. & Zuazua, E. (2022). Control of reaction-diffusion models in biology and social sciences. Math. Control Relat. Fields, 12(4), 955–1038. https://doi.org/10.3934/mcrf.2022032
• Esteve-Yagüe, C. & Zuazua, E. (2022). Differentiability with respect to the initial condition for Hamilton-Jacobi equations. SIAM J. Math. Anal., 54(5), 5388–5423. https://doi.org/10.1137/22M1469353
• Han, Z. & Zuazua, E. (2022). Slow decay and turnpike for infinite-horizon hyperbolic linear quadratic problems. SIAM J. Control Optim., 60(4), 2440–2468. https://doi.org/10.1137/21M1441985
• Biccari, U., Warma, M., & Zuazua, E. (2022). Control and numerical approximation of fractional diffusion equations. Numerical control. Part A.
• Liard, T. & Zuazua, E. (2022). Initial data identification for the one-dimensional Burgers equation. IEEE Trans. Autom. Control, 67(6), 3098–3104. https://doi.org/10.1109/TAC.2021.3096921
• Veldman, D. W. M. & Zuazua, E. (2022). A framework for randomized time-splitting in linear-quadratic optimal control. Numer. Math., 151(2), 495–549. https://doi.org/10.1007/s00211-022-01290-3
• Saraç, Y. & Zuazua, E. (2022). Sidewise profile control of 1-D waves. J. Optim. Theory Appl., 193(1-3), 931–949. https://doi.org/10.1007/s10957-021-01986-w
• Lance, G., Trélat, E., & Zuazua, E. (2022). Numerical issues and turnpike phenomenon in optimal shape design. Optimization and control for partial differential equations. Uncertainty quantification, open and closed-loop control, and shape optimization. https://doi.org/10.1515/9783110695984-012
• Ruiz-Balet, D., Affili, E., & Zuazua, E. (2022). Interpolation and approximation via momentum ResNets and neural ODEs. Syst. Control Lett., 162, 13. https://doi.org/10.1016/j.sysconle.2022.105182
• Jin, S., Zhu, Y., & Zuazua, E. (2022). The Vlasov-Fokker-Planck equation with high dimensional parametric forcing term. Numer. Math., 150(2), 479–519. https://doi.org/10.1007/s00211-021-01257-w
• Esteve-Yagüe, C., Geshkovski, B., Pighin, D., & Zuazua, E. (2022). Turnpike in Lipschitz-nonlinear optimal control. Nonlinearity, 35(4), 1652–1701. https://doi.org/10.1088/1361-6544/ac4e61
• Wang, G., Zhang, Y., & Zuazua, E. (2022). Flow decomposition for heat equations with memory. J. Math. Pures Appl. (9), 158, 183–215. https://doi.org/10.1016/j.matpur.2021.11.005
• Veldman, D. & Zuazua, E. (2022). Local Stability and Convergence of Unconstrained Model Predictive Control. (Unpublished, Submitted). arXiv: 2206.01097
• Crin-Barat, T., De Nitti, N., & Zuazua, E. (2022). On the decay of one-dimensional locally and partially dissipated hyperbolic systems. (Unpublished, Submitted). arXiv: 2206.00555
• Biccari, U., Esteve-Yagüe, C., & Oroya-Villalta, D. J. (2022). Multilevel selective harmonic modulation via optimal control. Appl. Math. Optim., 86(3), 30. https://doi.org/10.1007/s00245-022-09917-5
• Biccari, U., Warma, M., & Zuazua, E. (2022). Control and numerical approximation of fractional diffusion equations. Handbook of Numerical Analysis, Vol. 23.
• Biccari, U. (2022). Internal control for a non-local Schrödinger equation involving the fractional Laplace operator. Evol. Equ. Control Theory, 11(1), 301–324. https://doi.org/10.3934/eect.2021014
• Biccari, U., Hernández-Santamaria, V., & Vancostenoble, J. (2022). Existence and cost of boundary controls for a degenerate/singular parabolic equation. Math. Control Relat. Fields, 12(2), 495–530. https://doi.org/10.3934/mcrf.2021032
• Biccari, U. & Zuazua, E. (2022). Multilevel selective harmonic modulation by duality. IFAC-PapersOnLine, 55(16), 56–61.
• Lizama, C., Warma, M., & Zamorano, S. (2022). Exterior controllability properties for a fractional Moore-Gibson-Thompson equation. Fract. Calc. Appl. Anal., 25(3), 887–923. https://doi.org/10.1007/s13540-022-00018-2
• Arancibia, R., Lecaros, R., Mercado, A., & Zamorano, S. (2022). An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound. J. Inverse Ill-Posed Probl., 30(5), 659–675. https://doi.org/10.1515/jiip-2020-0090
• Chen, J., Liu, Z., Fiodar, E. L., & Obukhovskii, V. (2022). Optimal feedback control for a class of second-order evolution differential inclusions with Clarke's subdifferential. J. Nonlinear Var. Anal., 6, 551–565. https://doi.org/10.1016/j.cnsns.2023.107192
• Du, Z. & da Fonseca, C. M. (2022). A periodic determinantal property for \((0,1)\) double banded matrices. Linear Multilinear Algebra, 70(20), 5316–5328. https://doi.org/10.1080/03081087.2021.1913980
• da Fonseca, C. M. & Kowalenko, V. (2022). On tridiagonal matrices associated with Jordan blocks. Acta Univ. Sapientiae, Math., 14(1), 61–74. https://doi.org/10.2478/ausm-2022-0004
• Du, Z. & da Fonseca, C. M. (2022). An identity involving derangement numbers and Bell numbers. Appl. Anal. Discrete Math., 16(2), 485–494. https://doi.org/10.2298/AADM200705010D
• Andelic, M., Da Fonseca, C. M., Kilic, E., & Stanic, Z. (2022). A Sylvester-Kac matrix type and the Laplacian controllability of half graphs. Electron. J. Linear Algebra, 38, 559–571.
• Du, Z., da Fonseca, C. M., & Pereira, A. (2022). On determinantal recurrence relations of banded matrices. Kuwait J. Sci., 49(1), 9. https://doi.org/10.48129/kjs.v49i1.11165
• Du, Z., Dimitrov, D., & da Fonseca, C. M. (2022). New strong divisibility sequences. Ars Math. Contemp., 22(1), 13. https://doi.org/10.26493/1855-3974.2473.f2e

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2021

• Bárcena-Petisco, J. A. & Zuazua, E. (2021). Averaged dynamics and control for heat equations with random diffusion. Syst. Control Lett., 158, 15. https://doi.org/10.1016/j.sysconle.2021.105055
• Sakamoto, N. & Zuazua, E. (2021). The turnpike property in nonlinear optimal control — a geometric approach. Automatica, 134, 11. https://doi.org/10.1016/j.automatica.2021.109939
• Ko, D. & Zuazua, E. (2021). Model predictive control with random batch methods for a guiding problem. Math. Models Methods Appl. Sci., 31(8), 1569–1592. https://doi.org/10.1142/S0218202521500329
• Heiland, J. & Zuazua, E. (2021). Classical system theory revisited for turnpike in standard state space systems and impulse controllable descriptor systems. SIAM J. Control Optim., 59(5), 3600–3624. https://doi.org/10.1137/20M1356105
• Geshkovski, B. & Zuazua, E. (2021). Controllability of one-dimensional viscous free boundary flows. SIAM J. Control Optim., 59(3), 1830–1850. https://doi.org/10.1137/19M1285354
• Gugat, M., Schuster, M., & Zuazua, E. (2021). The finite-time turnpike phenomenon for optimal control problems: stabilization by non-smooth tracking terms. Stabilization of distributed parameter systems: design methods and applications. Selected papers based on the presentations of the mini-symposium at ICIAM 2019, Valencia, Spain, July 15–19, 2019. https://doi.org/10.1007/978-3-030-61742-4_2
• Lohéac, J., Trélat, E., & Zuazua, E. (2021). Nonnegative control of finite-dimensional linear systems. Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 38(2), 301–346. https://doi.org/10.1016/j.anihpc.2020.07.004
• Zamorano, S. (2021). Approximate controllability from the exterior for a nonlocal Sobolev-Galpern type equation. Math. Notes, 110(4), 609–622. https://doi.org/10.1134/S0001434621090315
• Warma, M. & Zamorano, S. (2021). Exponential turnpike property for fractional parabolic equations with non-zero exterior data. ESAIM, Control Optim. Calc. Var., 27, 35. https://doi.org/10.1051/cocv/2020076
• Dardé, J., Ervedoza, S., & Morales, R. (2021). Uniform null controllability for parabolic equations with discontinuous diffusion coefficients. ESAIM, Control Optim. Calc. Var., 27, 29. https://doi.org/10.1051/cocv/2021063
• da Fonseca, C. M. (2021). Some comments on the properties of a particular tridiagonal matrix. J. Discrete Math. Sci. Cryptography, 24(1), 49–51. https://doi.org/10.1080/09720529.2019.1669920
• da Fonseca, C. M. (2021). On some quasi anti-tridiagonal matrices. J. Discrete Math. Sci. Cryptography, 24(4), 1043–1052. https://doi.org/10.1080/09720529.2020.1859800
• Du, Z., da Fonseca, C. M., Xu, Y., & Ye, J. (2021). Disproving a conjecture of Thornton on Bohemian matrices. Open Math., 19, 505–514. https://doi.org/10.1515/math-2021-0045
• Anđjelić, M. & da Fonseca, C. M. (2021). Some determinantal considerations for pentadiagonal matrices. Linear Multilinear Algebra, 69(16), 3121–3129. https://doi.org/10.1080/03081087.2019.1708845
• da Fonseca, C. M. & K\il\iç, E. (2021). A new type of Sylvester-Kac matrix and its spectrum. Linear Multilinear Algebra, 69(6), 1072–1082. https://doi.org/10.1080/03081087.2019.1620673

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2020

• Biccari, U., Marica, A., & Zuazua, E. (2020). Propagation of one- and two-dimensional discrete waves under finite difference approximation. Found. Comput. Math., 20(6), 1401–1438. https://doi.org/10.1007/s10208-020-09445-0
• Monge, A. & Zuazua, E. (2020). Sparse source identification of linear diffusion-advection equations by adjoint methods. Syst. Control Lett., 145, 10. https://doi.org/10.1016/j.sysconle.2020.104801
• Esteve, C. & Zuazua, E. (2020). The inverse problem for Hamilton-Jacobi equations and semiconcave envelopes. SIAM J. Math. Anal., 52(6), 5627–5657. https://doi.org/10.1137/20M1330130
• Ko, D. & Zuazua, E. (2020). Asymptotic behavior and control of a “Guidance by repulsion'' model. Math. Models Methods Appl. Sci., 30(4), 765–804. https://doi.org/10.1142/S0218202520400047
• Ruiz-Balet, D. & Zuazua, E. (2020). Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations. J. Math. Pures Appl. (9), 143, 345–375. https://doi.org/10.1016/j.matpur.2020.08.006
• Lance, G., Trélat, E., & Zuazua, E. (2020). Shape turnpike for linear parabolic PDE models. Syst. Control Lett., 142, 8. https://doi.org/10.1016/j.sysconle.2020.104733
• Cortés, J., Navarro-Quiles, A., Romero, J., Roselló, M., & Zuazua, E. (2020). Full probabilistic solution of a finite dimensional linear control system with random initial and final conditions. J. Franklin Inst., 357(12), 8156–8180. https://doi.org/10.1016/j.jfranklin.2020.06.005
• Biccari, U., Warma, M., & Zuazua, E. (2020). Controllability of the one-dimensional fractional heat equation under positivity constraints. Commun. Pure Appl. Anal., 19(4), 1949–1978. https://doi.org/10.3934/cpaa.2020086
• Hernández-Santamaría, V. & Zuazua, E. (2020). Controllability of shadow reaction-diffusion systems. J. Differ. Equations, 268(7), 3781–3818. https://doi.org/10.1016/j.jde.2019.10.012
• Biccari, U., Navarro-Quiles, A., & Zuazua, E. (2020). Stochastic optimization methods for the simultaneous control of parameter-dependent systems. (Unpublished, Submitted). arXiv: 2005.04116
• Zuazua, E. (2020). Asymptotic behavior of scalar convection-diffusion equations. (Unpublished, Submitted). arXiv: 2003.11834
• Biccari, U., Marica, A., & Zuazua, E. (2020). Propagation of one- and two-dimensional discrete waves under finite difference approximation. Found. Comput. Math., 20(6), 1401–1438. https://doi.org/10.1007/s10208-020-09445-0
• Biccari, U. & Warma, M. (2020). Null-controllability properties of a fractional wave equation with a memory term. Evol. Equ. Control Theory, 9(2), 399–430. https://doi.org/10.3934/eect.2020011
• Biccari, U., Warma, M., & Zuazua, E. (2020). Controllability of the one-dimensional fractional heat equation under positivity constraints. Commun. Pure Appl. Anal., 19(4), 1949–1978. https://doi.org/10.3934/cpaa.2020086
• Biccari, U. & Zuazua, E. (2020). A stochastic approach to the synchronization of coupled oscillators. Frontiers in Energy Research, 8, 115.

Lecaros, R., López-Ríos, J., Ortega, J. H., & Zamorano, S. (2020). The stability for an inverse problem of bottom recovering in water-waves. Inverse Probl., 36(11), 22. https://doi.org/10.1088/1361-6420/abafee

Warma, M. & Zamorano, S. (2020). Analysis of the controllability from the exterior of strong damping nonlocal wave equations. ESAIM, Control Optim. Calc. Var., 26, 34. https://doi.org/10.1051/cocv/2019028

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2019

• Maity, D., Tucsnak, M., & Zuazua, E. (2019). Controllability of a class of infinite dimensional systems with age structure. Control Cybern., 48(2), 231–260.
• Ruiz-Balet, D. & Zuazua, E. (2019). A parabolic approach to the control of opinion spreading. Applied wave mathematics II. Selected topics in solids, fluids, and mathematical methods and complexity. https://doi.org/10.1007/978-3-030-29951-4_15
• Biccari, U., Ko, D., & Zuazua, E. (2019). Dynamics and control for multi-agent networked systems: a finite-difference approach. Math. Models Methods Appl. Sci., 29(4), 755–790. https://doi.org/10.1142/S0218202519400050
• Pighin, D. & Zuazua, E. (2019). Controllability under positivity constraints of multi-d wave equations. Trends in control theory and partial differential equations. https://doi.org/10.1007/978-3-030-17949-6_11
• Morales-Hernández, M. & Zuazua, E. (2019). Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids. Comput. Appl. Math., 38(4), 25. https://doi.org/10.1007/s40314-019-0935-0
• Maity, D., Tucsnak, M., & Zuazua, E. (2019). Controllability and positivity constraints in population dynamics with age structuring and diffusion. J. Math. Pures Appl. (9), 129, 153–179. https://doi.org/10.1016/j.matpur.2018.12.006
• Privat, Y., Trélat, E., & Zuazua, E. (2019). Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions. Calc. Var. Partial Differ. Equ., 58(2), 45. https://doi.org/10.1007/s00526-019-1522-3
• Lissy, P. & Zuazua, E. (2019). Internal observability for coupled systems of linear partial differential equations. SIAM J. Control Optim., 57(2), 832–853. https://doi.org/10.1137/17M1119160
• Bianchini, R., Gosse, L., & Zuazua, E. (2019). A two-dimensional “flea on the elephant'' phenomenon and its numerical visualization. Multiscale Model. Simul., 17(1), 137–166. https://doi.org/10.1137/18M1179985
• Pouchol, C., Trélat, E., & Zuazua, E. (2019). Phase portrait control for 1D monostable and bistable reaction-diffusion equations. Nonlinearity, 32(3), 884–909. https://doi.org/10.1088/1361-6544/aaf07e
• Hernández-Santamaría, V., Lazar, M., & Zuazua, E. (2019). Greedy optimal control for elliptic problems and its application to turnpike problems. Numer. Math., 141(2), 455–493. https://doi.org/10.1007/s00211-018-1005-z
• Biccari, U. & Hernández-Santamaria, V. (2019). Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects. IMA J. Math. Control Inf., 36(4), 1199–1235. https://doi.org/10.1093/imamci/dny025
• Biccari, U., Ko, D., & Zuazua, E. (2019). Dynamics and control for multi-agent networked systems: a finite-difference approach. Math. Models Methods Appl. Sci., 29(4), 755–790. https://doi.org/10.1142/S0218202519400050
• Biccari, U. (2019). Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential. Math. Control Relat. Fields, 9(1), 191–219. https://doi.org/10.3934/mcrf.2019011
• Biccari, U. & Hernández-Santamaria, V. (2019). Null controllability of Linear and semilinear nonlocal heat equations with an additive integral kernel. SIAM J. Control Optim., 57(4), 2924–2938. https://doi.org/10.1137/18M1218431
• Biccari, U. & Micu, S. (2019). Null-controllability properties of the wave equation with a second order memory term. J. Differ. Equations, 267(2), 1376–1422. https://doi.org/10.1016/j.jde.2019.02.009
• Warma, M. & Zamorano, S. (2019). Null controllability from the exterior of a one-dimensional nonlocal heat equation. Control Cybern., 48(3), 417–438.
• Lizama, C. & Zamorano, S. (2019). Controllability results for the Moore-Gibson-Thompson equation arising in nonlinear acoustics. J. Differ. Equations, 266(12), 7813–7843. https://doi.org/10.1016/j.jde.2018.12.017

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2018

• Trélat, E., Zhang, C., & Zuazua, E. (2018). Optimal shape design for 2D heat equations in large time. Pure Appl. Funct. Anal., 3(1), 255–269.
• Pighin, D. & Zuazua, E. (2018). Controllability under positivity constraints of semilinear heat equations. Math. Control Relat. Fields, 8(3-4), 935–964. https://doi.org/10.3934/mcrf.2018041
• Biccari, U., Warma, M., & Zuazua, E. (2018). Local regularity for fractional heat equations. Recent advances in PDEs: analysis, numerics and control. In honor of Prof. Fernández-Cara’s 60th birthday. Based on talks given at the workshop, Sevilla, Spain, January 25–27, 2017. https://doi.org/10.1007/978-3-319-97613-6_12
• Trélat, E., Zhu, J., & Zuazua, E. (2018). Allee optimal control of a system in ecology. Math. Models Methods Appl. Sci., 28(9), 1665–1697. https://doi.org/10.1142/S021820251840002X
• Lohéac, J., Trélat, E., & Zuazua, E. (2018). Minimal controllability time for finite-dimensional control systems under state constraints. Automatica, 96, 380–392. https://doi.org/10.1016/j.automatica.2018.07.010
• Lissy, P. & Zuazua, E. (2018). Internal controllability for parabolic systems involving analytic non-local terms. Chin. Ann. Math., Ser. B, 39(2), 281–296. https://doi.org/10.1007/s11401-018-1064-6
• Trélat, E., Zhang, C., & Zuazua, E. (2018). Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces. SIAM J. Control Optim., 56(2), 1222–1252. https://doi.org/10.1137/16M1097638
• Biccari, U., Warma, M., & Zuazua, E. (2018). Local regularity for fractional heat equations. Recent advances in PDEs: analysis, numerics and control. In honor of Prof. Fernández-Cara’s 60th birthday. Based on talks given at the workshop, Sevilla, Spain, January 25–27, 2017. https://doi.org/10.1007/978-3-319-97613-6_12
• Biccari, U. & Hernandez-Santamaria, V. (2018). The Poisson equation from non-local to local. Electron. J. Differ. Equ., 2018, 13.
• Zamorano, S. (2018). Turnpike property for two-dimensional Navier-Stokes equations. J. Math. Fluid Mech., 20(3), 869–888. https://doi.org/10.1007/s00021-018-0382-5
• Carreño, N., Morales, R., & Osses, A. (2018). Potential reconstruction for a class of hyperbolic systems from incomplete measurements. Inverse Probl., 34(8), 18. https://doi.org/10.1088/1361-6420/aac6a9

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2017

• Han, Z. & Zuazua, E. (2017). Decay rates for elastic-thermoelastic star-shaped networks. Netw. Heterog. Media, 12(3), 461–488. https://doi.org/10.3934/nhm.2017020
• Biccari, U., Warma, M., & Zuazua, E. (2017). Addendum to: "Local elliptic regularity for the Dirichlet fractional Laplacian". Adv. Nonlinear Stud., 17(4), 837–839. https://doi.org/10.1515/ans-2017-6020
• Lü, Q., Zhang, X., & Zuazua, E. (2017). Null controllability for wave equations with memory. J. Math. Pures Appl. (9), 108(4), 500–531. https://doi.org/10.1016/j.matpur.2017.05.001
• Privat, Y., Trélat, E., & Zuazua, E. (2017). Optimal location of sensors and actuators for wave and heat processes. PDE’s, dispersion, scattering theory and control theory.
• Chaves-Silva, F. W., Zhang, X., & Zuazua, E. (2017). Controllability of evolution equations with memory. SIAM J. Control Optim., 55(4), 2437–2459. https://doi.org/10.1137/151004239
• Lohéac, J., Trélat, E., & Zuazua, E. (2017). Minimal controllability time for the heat equation under unilateral state or control constraints. Math. Models Methods Appl. Sci., 27(9), 1587–1644. https://doi.org/10.1142/S0218202517500270
• Gosse, L. & Zuazua, E. (2017). Filtered gradient algorithms for inverse design problems of one-dimensional Burgers equation. Innovative algorithms and analysis. Based on the presentations at the workshop, Rome, Italy, May 17–20, 2016. https://doi.org/10.1007/978-3-319-49262-9_7
• Privat, Y., Trélat, E., & Zuazua, E. (2017). Actuator design for parabolic distributed parameter systems with the moment method. SIAM J. Control Optim., 55(2), 1128–1152. https://doi.org/10.1137/16M1058418
• Biccari, U., Warma, M., & Zuazua, E. (2017). Local elliptic regularity for the Dirichlet fractional Laplacian. Adv. Nonlinear Stud., 17(2), 387–409. https://doi.org/10.1515/ans-2017-0014
• Lohéac, J. & Zuazua, E. (2017). Averaged controllability of parameter dependent conservative semigroups. J. Differ. Equations, 262(3), 1540–1574. https://doi.org/10.1016/j.jde.2016.10.017
• Porretta, A. & Zuazua, E. (2017). Numerical hypocoercivity for the Kolmogorov equation. Math. Comput., 86(303), 97–119. https://doi.org/10.1090/mcom/3157
• Biccari, U., Warma, M., & Zuazua, E. (2017). Addendum: “Local elliptic regularity for the Dirichlet fractional Laplacian''. Adv. Nonlinear Stud., 17(4), 837–839. https://doi.org/10.1515/ans-2017-6020
• Biccari, U., Warma, M., & Zuazua, E. (2017). Local elliptic regularity for the Dirichlet fractional Laplacian. Adv. Nonlinear Stud., 17(2), 387–409. https://doi.org/10.1515/ans-2017-0014
• Beretta, E., Cavaterra, C., Ortega, J. H., & Zamorano, S. (2017). Size estimates of an obstacle in a stationary Stokes fluid. Inverse Probl., 33(2), 29. https://doi.org/10.1088/1361-6420/33/2/025008

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2016

• Privat, Y., Trélat, E., & Zuazua, E. (2016). Randomised observation, control and stabilization of waves. ZAMM, Z. Angew. Math. Mech., 96(5), 538–549. https://doi.org/10.1002/zamm.201500181
• Escobedo, R., Ibañez, A., & Zuazua, E. (2016). Optimal strategies for driving a mobile agent in a “guidance by repulsion'' model. Commun. Nonlinear Sci. Numer. Simul., 39, 58–72. https://doi.org/10.1016/j.cnsns.2016.02.017
• Ervedoza, S., Marica, A., & Zuazua, E. (2016). Numerical meshes ensuring uniform observability of one-dimensional waves: construction and analysis. IMA J. Numer. Anal., 36(2), 503–542. https://doi.org/10.1093/imanum/drv026
• Porretta, A. & Zuazua, E. (2016). Remarks on long time versus steady state optimal control. Mathematical paradigms of climate science. Based on the workshop, Rome, Italy, summer 2013. https://doi.org/10.1007/978-3-319-39092-5_5
• Han, Z. & Zuazua, E. (2016). Decay rates for \(1-d\) heat-wave planar networks. Netw. Heterog. Media, 11(4), 655–692. https://doi.org/10.3934/nhm.2016013
• Gugat, M. & Zuazua, E. (2016). Exact penalization of terminal constraints for optimal control problems. Optim. Control Appl. Methods, 37(6), 1329–1354. https://doi.org/10.1002/oca.2238
• Choulli, M. & Zuazua, E. (2016). Lipschitz dependence of the coefficients on the resolvent and greedy approximation for scalar elliptic problems. C. R., Math., Acad. Sci. Paris, 354(12), 1174–1187. https://doi.org/10.1016/j.crma.2016.10.017
• Beli, C. N., Ignat, L. I., & Zuazua, E. (2016). Dispersion for 1-D Schrödinger and wave equations with BV coefficients. Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 33(6), 1473–1495. https://doi.org/10.1016/j.anihpc.2015.06.002
• Lazar, M. & Zuazua, E. (2016). Greedy controllability of finite dimensional linear systems. Automatica, 74, 327–340. https://doi.org/10.1016/j.automatica.2016.08.010
• Lohéac, J. & Zuazua, E. (2016). From averaged to simultaneous controllability. Ann. Fac. Sci. Toulouse, Math. (6), 25(4), 785–828. https://doi.org/10.5802/afst.1511
• Allahverdi, N., Pozo, A., & Zuazua, E. (2016). Numerical aspects of large-time optimal control of Burgers equation. ESAIM, Math. Model. Numer. Anal., 50(5), 1371–1401. https://doi.org/10.1051/m2an/2015076
• Fernández-Cara, E., Lü, Q., & Zuazua, E. (2016). Null controllability of linear heat and wave equations with nonlocal spatial terms. SIAM J. Control Optim., 54(4), 2009–2019. https://doi.org/10.1137/15M1044291
• Lü, Q. & Zuazua, E. (2016). On the lack of controllability of fractional in time ODE and PDE. Math. Control Signals Syst., 28(2), 21. https://doi.org/10.1007/s00498-016-0162-9
• Allahverdi, N., Pozo, A., & Zuazua, E. (2016). Numerical aspects of sonic-boom minimization. A panorama of mathematics: pure and applied. Conference mathematics and its applications, Kuwait University, Safat, Kuwait, November 14–17, 2014. https://doi.org/10.1090/conm/658/13133
• Biccari, U. & Zuazua, E. (2016). Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function. J. Differ. Equations, 261(5), 2809–2853. https://doi.org/10.1016/j.jde.2016.05.019
• Zuazua, E. (2016). Stable observation of additive superpositions of partial differential equations. Syst. Control Lett., 93, 21–29. https://doi.org/10.1016/j.sysconle.2016.02.017
• Privat, Y., Trélat, E., & Zuazua, E. (2016). Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains. J. Eur. Math. Soc. (JEMS), 18(5), 1043–1111. https://doi.org/10.4171/JEMS/608
• Lecaros, R. & Zuazua, E. (2016). Control of 2D scalar conservation laws in the presence of shocks. Math. Comput., 85(299), 1183–1224. https://doi.org/10.1090/mcom/3015
• Gugat, M., Trélat, E., & Zuazua, E. (2016). Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property. Syst. Control Lett., 90, 61–70. https://doi.org/10.1016/j.sysconle.2016.02.001
• Lü, Q. & Zuazua, E. (2016). Averaged controllability for random evolution Partial Differential Equations. J. Math. Pures Appl. (9), 105(3), 367–414. https://doi.org/10.1016/j.matpur.2015.11.004
• Biccari, U. & Zuazua, E. (2016). Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function. J. Differ. Equations, 261(5), 2809–2853. https://doi.org/10.1016/j.jde.2016.05.019

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