Publications

2026

• Zuazua, E. (2026). Machine Learning and Control: Foundations, Advances, and Perspectives. arXiv preprint. arXiv: 2510.03303 , FAU CRIS
• Alcalde, A., Fantuzzi, G., & Zuazua, E. (2026). Exact sequence interpolation with transformers. (Unpublished, Submitted). arXiv: 2502.02270 , 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 (Unpublished, Submitted).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 Iriondo, E., & 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 (Unpublished, Submitted).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

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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 (Unpublished, Submitted).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 (Unpublished, Submitted).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
• Ignat, L. & Zuazua, E. (2025). Sharp Numerical Approximation of the Hardy Constant. Discrete and Continuous Dynamical Systems. https://doi.org/10.3934/dcds.2025165
• Li, Z., Liu, K., Song, Y., Yue, H., & Zuazua, E. (2025). Deep Neural ODE Operator Networks for PDEs. arXiv preprint.
• 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
• Liverani, L., Steynberg, M., & Zuazua, E. (2025). HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling. arXiv preprint. arXiv: 2509.14123
• Ftouhi, I. & Zuazua, E. (2025). Sensor Placement via Large Deviations in the Eikonal Equation. arXiv preprint. arXiv: 2508.21469
• 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
• Sonego, M. & Zuazua, E. (2025). Control of a Lotka-Volterra System with Weak Competition. Communications in Information and Systems (CIS). arXiv: 2409.20279
• 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
• Ignat, L. I. & Zuazua, E. (2025). Optimal convergence rates for the finite element approximation of the Sobolev constant. (Unpublished, Submitted). arXiv: 2504.09637
• 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. & Ram\’\irez-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

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2024

• Alvarez-López Antonio, O. R. & Zuazua, E. (2024). Optimized classification with neural ODEs via separability. (Unpublished, Submitted). arXiv: https://doi.org/10.48550/arXiv.2312.13807 , FAU CRIS
• 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
• Zamorano, S. & Zuazua, E. (2024). Tracking controllability for finite-dimensional linear systems. (Unpublished, Submitted). arXiv: 2407.18641
• 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. (Unpublished, Submitted). 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

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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

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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
• Francisco, A., Biccari, U., & Zuazua, E. (2022). Computational performance of the MMOC in the inverse design of the Doswell frontogenesis equation. (Unpublished, Submitted). arXiv: 2210.03798
• 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-Santamar\’\ia, 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

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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
• Biccari, U. & Zuazua, E. (2021). Multilevel Selective Harmonic Modulation by Duality. (Unpublished, Submitted). arXiv: 2112.10443
• 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

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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-Santamar\’\ia, 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-Santamar\’\ia, 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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