Publications

Neural ODE Control for Classification, Approximation and Transport

data classification, deep learning, Neural ODEs, Optimal Transport, simultaneous control, transport equations, universal approximation, Wasserstein distance

Ruiz-Balet D., Zuazua E. Neural ODE Control for Classification, Approximation and Transport (2022). SIAM Review Abstract. We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address…

Controllability and Positivity Constraints in Population Dynamics with age, size Structuring and Diffusion

Yacouba Simporé, Umberto Biccari. Controllability and Positivity Constraints in Population Dynamics with age, size Structuring and Diffusion (2022) Abstract. In this article, we consider the infinite dimensional linear control system…

Null Controllability for a Degenerate Structured Population Model

Yacouba Simporé, Yassine El gantouh, Umberto Biccari. Null Controllability for a Degenerate Structured Population Model (2022) Abstract. In this paper, we consider the infinite dimensional linear control system describing population…

Greedy search of optimal approximate solutions

M. Lazar, E. Zuazua. Greedy search of optimal approximate solutions (2022) Commun. Optim. Theory Abstract. In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed…

Control of reaction-diffusion models in biology and social sciences

comparison principle, Constraints, Control, Mathematical biology, paths of steady-states, phase plane, Reaction-diffusion, traveling waves

Domènec Ruiz-Balet, Enrique Zuazua. Control of reaction-diffusion models in biology and social sciences (2022) Math. Control Relat. Fields Abstract. These lecture notes address the controllability under state constraints of reaction-diffusion equations…

Optimal actuator design via Brunovsky’s normal form

Brunovsky normal form, Controllability, finite-dimensional systems, Kalman rank condition, lumped control, optimal actuator design.

B. Geshkovski, E. Zuazua, Optimal actuator design via Brunovsky's normal form IEEE Automatic Control (2022) DOI: 10.1109/TAC.2022.3181222 Abstract: In this paper, by using the Brunovsky normal form, we provide a…

Turnpike in Optimal Control PDES, ResNets, and beyond

Brunovsky normal form, Controllability, finite-dimensional systems, Kalman rank condition, lumped control, optimal actuator design.

B. Geshkovski, E. Zuazua, Turnpike in Optimal Control PDES, ResNets and beyond (2022) Acta Numer., Vol. 31, pp. 135-263. doi:10.1017/S0962492922000046 Abstract: The turnpike property in contemporary macroeconomics asserts that if…

Local Stability and Convergence of Unconstrained Model Predictive Control

Daniël Veldman, Enrique Zuazua. Local Stability and Convergence of Unconstrained Model Predictive Control (2022) Abstract. The local stability and convergence for Model Predictive Control (MPC) of unconstrained nonlinear dynamics based on…

Preface- Control and Analysis of Partial Differential Equations

Nicolae Cîndea, Günter Leugering, Jëróme Lohêac, Sorin Micu, Kirsten Morris, Takeo Takahashi and Enrique Zuazua. Preface- Control and Analysis of Partial Differential Equations, Marius Tucsbak 60th Anniversary Volume (2022) Math.…

On the decay of one-dimensional locally and partially dissipated and hyperbolic systems

Crin-Barat T., De Nitti N., Zuazua E.. On the decay of one-dimensional locally and partially dissipated and hyperbolic systems (2022) Abstract. We study the time-asymptotic behavior of linear hyperbolic systems…

A framework for randomized time-splitting in linear-quadratic optimal control

Daniël Veldman, Enrique Zuazua. (2022) Numerische Mathematik. DOI: https://doi.org/10.1007/s00211-022-01290-3 Abstract. Inspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems,…

Nonuniqueness of minimizers for semilinear optimal control problems

D. Pighin. Nonuniqueness of minimizers for semilinear optimal control problems (2022) J. Eur. Math. Soc, , published online first. https://doi.org/10.4171/jems/1232 Abstract. A counterexample to uniqueness of global minimizers of semilinear…

The turnpike property and the longtime behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems

C. Esteve, H. Kouhkouh, D. Pighin, E. Zuazua. The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems. Math. Control Signals Syst. (2022). https://doi.org/10.1007/s00498-022-00325-2 Abstract:…

Numerical Control: Part A

Emmanuel Trélat, Enrique Zuazua. Numerical Control: Part A First Edition (2022), Elsevier Science & Technology. Handbook of Numerical Analysis XXIII, Vol. 23, p. 1-558, eBook ISBN: 9780323853392, Hardcover ISBN: 9780323850599…

Interpolation and approximation via Momentum ResNets and Neural ODEs

Domènec Ruiz-Balet, Elisa Affili , Enrique Zuazua. Interpolation and approximation via Momentum ResNets and Neural ODEs IEEE Control Syst. Lett. (2022) Vol. 162, ISSN 0167-6911, https://doi.org/10.1016/j.sysconle.2022.105182 Abstract. In this article,…

Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

Esteve C., Zuazua E.. Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws (2022) Abstract. We give a full characterization of the range of the operator which…

Linear projection-based CEST parameter estimation

F. Glang, Moritz Fabian, A. German, Katrin M Khakzar, A. Mennecke, A. Liebert, K. Herz, P. Liebig, B. Kasper, Manuel Schmidt, E. Zuazua, A. Nagel, F. Laun, A. Dörfler, K.…

Turnpike in Lipschitz-nonlinear optimal control

Esteve C., Geshkovski G., Pighin D., Zuazua E. . Turnpike in Lipschitz-nonlinear optimal control Nonlinearity. Vol 5. No. 34, pp. 1652-1701 (2022) https://doi.org/10.1088/1361-6544/ac4e61 Abstract. We present a new proof of…

The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term

Shi Jin, Yuhua Zhu, Enrique Zuazua. The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term Numer. Math. 150, 479–519 (2022). https://doi.org/10.1007/s00211-021-01257-w Abstract. We consider the Vlasov-Fokker-Planck equation with random electric…

Analysis and numerical solvability of backward-forward conservation laws

Thibault Liard, Enrique Zuazua. Analysis and numerical solvability of backward-forward conservation laws (2022) Abstract. In this paper, we study the problem of initial data identification for weak-entropy solutions of the…

A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation

U. Biccari, Y. Song, X. Yuan, E. Zuazua. A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation (2022) Abstract. We consider the problem of identifying…

Control and Numerical approximation of Fractional Diffusion Equations

Exterior Control, Finite Element Method, Fractional diffusion equation, Fractional Laplacian, Interior Control, Numerical approximation, simultaneous control

Umberto Biccari, Mahamadi Warma, Enrique Zuazua. Control and Numerical approximation of Fractional Diffusion Equations (2022) Handb. Numer. Anal. Elsevier. ISSN:1570-8659, DOI: https://doi.org/10.1016/bs.hna.2021.12.001 Abstract. The aim of this work is to give…

Flow decomposition for heat equations with memory

decomposition of the flow, Heat equations with memory, hybrid parabolichyperbolic phenomenon

G. Wang, Y. Zhang, E. Zuazua. Flow decomposition for heat equations with memory (2022) J. Math. Pures Appl, Vol. 158, pp 183-215, ISSN:0021-7824. https://doi.org/10.1016/j.matpur.2021.11.005 Abstract. We build up a decomposition…

Sidewise control of 1-d waves

1-d wave equations, BV-coefficients, nodal profile con-trol, sidewise controllability, sidewise energy estimates

Y. Sarac, E. Zuazua. Sidewise control of 1-d waves. J Optim Theory Appl (2022). https://doi.org/10.1007/s10957-021-01986-w Abstract. We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control…

Constrained control of gene-flow models

bistable equations, Control, geneflow models, non-controllability, reaction-diffusion equations, spatial heterogeneity, staircase method

Mazari I., Ruiz-Balet D., Zuazua E.. Constrained control of gene-flow models. (2021) Ann. Inst. Henri Poincare (C) Anal. Non Lineaire ⟨hal-02373668⟩ Abstract. In ecology and population dynamics, gene-flow refers to…

Multilevel selective harmonic modulation by duality

Biccari U, Zuazua E. Multilevel selective harmonic modulation by duality (2021) Abstract. We address the Selective Harmonic Modulation (SHM) problem in power electronic engineering, consisting in designing a multilevel staircase…

Sparse approximation in learning via neural ODEs

deep learning, Neural ODEs, Nonlinear systems, optimal control, Sparsity, Supervised Learning

Esteve C., Geshkovski B. Sparse approximation in learning via neural ODEs (2021) Abstract. We consider the continuous-time, neural ordinary differential equation (neural ODE) perspective of deep supervised learning, and study the…

Averaged dynamics and control for heat equations with random diffusion

Bárcena J.A., Zuazua E.. Averaged dynamics and control for heat equations with random diffusion (2021) Syst. Control. Lett. Vol. 158. https://doi.org/10.1016/j.sysconle.2021.105055 Abstract. This paper deals with the averaged dynamics for…

Differentiability with respect to the initial condition for Hamilton-Jacobi equations

Esteve C., Zuazua E.. Differentiability with respect to the initial condition for Hamilton-Jacobi equations (2021) Abstract. We prove that the viscosity solution to a Hamilton-Jacobi equation with a smooth convex…

Control of certain parabolic models from biology and social sciences

Domènec Ruiz-Balet, , Enrique Zuazua. Control of certain parabolic models from biology and social sciences (2021) Abstract. These lecture notes address the controllability under state constraints of reaction-diffusion equations arising…

Special issue in the honor of Enrique Zuazua’s 60th birthday

G. Buttazzo, E. Casas, L. de Teresa, R. Glowinski, G. Leugering, E. Trélat and X. Zhang (eds.). Special issue in the honor of Enrique Zuazua's 60th birthday (2021) ESAIM: Control, Optimisation…

Multilevel control by duality

Umberto Biccari, Enrique Zuazua. Multilevel control by duality (2021) Abstract. We discuss the multilevel control problem for linear dynamical systems, consisting in designing a piece-wise constant control function taking values in…

Model predictive control with random batch methods for a guiding problem

Agent-based models, Guiding problem, large scale complex systems, Random

Ko Dongnam, Zuazua Enrique. Model predictive control with random batch methods for a guiding problem (2021). Math. Models Methods Appl. Sci., Vol. 31, No. 8, pp. 1569-1592. (2021) DOI: https://doi.org/10.1142/S0218202521500329…

Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems

descriptor systems, linear systems, long time behavior, optimal control, Riccati equations

Heiland J., Zuazua E. Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems (2021) SIAM J. Control Optim., Vol. 59.5 (2021), pp. 3600-3624 Abstract.…

Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems

optimal control problems, Riccati operator, slow decay rate, turnpike property, weak controllability and observability

Zhong-Jie Han, E. Zuazua, Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems (2021) Abstract: This paper is devoted to analysing the explicit slow decay rate and turnpike in the…

Optimal control for neural ODE in a long time horizon and applications to the classification and simultaneous controllability problems

Jon Asier Bárcena-Petisco. Optimal control for neural ODE in a long time horizon and applications to the classification (2021) Abstract. We study the optimal control in a long time horizon…

The turnpike property in nonlinear optimal control – A geometric approach

Nonlinear system, optimal control, Turnpike

N. Sakamoto, E. Zuazua. The turnpike property in nonlinear optimal control - A geometric approach. (2021) Automatica., Vol. 134 (2021), p. 109939 Abstract: This paper presents, using dynamical system theory,…

A quantitative analysis of Koopman operator methods for system identification and predictions

Christophe Zhang, Enrique Zuazua. A quantitative analysis of Koopman operator methods for system identification and predictions (2021) Abstract. We give convergence and cost estimates for a data-driven system identification method:…

Optimal control of linear non-local parabolic problems with an integral kernel

Umberto Biccari, Víctor Hernández-Santamaría, Loic Louison, Abdennebi Omrane. Optimal control of linear non-local parabolic problems with an integral kernel. (2021) Abstract. We consider a linear non-local heat equation in a bounded…

Blow-up results for a logarithmic pseudo-parabolic p(.)-Laplacian type equation

Abita Rahmoune, Umberto Biccari. Blow-up results for a logarithmic pseudo-parabolic -Laplacian equation. (2021) Abstract. In this paper, we consider an initial-boundary value problem for the following mixed pseudo-parabolic p(.)-Laplacian type equation…

Local null controllability of the penalized Boussinesq system with a reduced number of controls

J.A. Bárcena-Petisco, Kevin Le Balc'H. Local null controllability of the penalized Boussinesq system with a reduced number of controls (2021) Abstract. In this paper we consider the Boussinesq system with homogeneous…

Initial data identification for the one-dimensional Burgers equation

Thibault Liard, Enrique Zuazua. Initial data identification for the one-dimensional Burgers equation. (2022). IEEE T Automat. Contr., Vol. 67, No. 6, pp. 3098-3104, DOI: 10.1109/TAC.2021.3096921 Abstract. In this paper, we…

Control of Hyperbolic and Parabolic Equations on Networks and Singular limits

advection-diffusion equations, Controllability, cost of controllability, network, singular limits, vanishing viscosity

J.A. Bárcena-Petisco, M. Cavalcante, G.M. Coclite, N. de Nitti, Enrique Zuazua. Control of Hyperbolic and Parabolic Equations on Networks and Singular limits (2021) Abstract. We study the controllability properties of the…

Controllability of one-dimensional viscous free boundary flows

B. Geshkovski, E. Zuazua. Controllability of one-dimensional viscous free boundary flows. Siam. J. Control. Optim (2021), Vol. 59, No. 3, pp. 1830–1850. https://doi.org/10.1137/19M1285354 Abstract. In this work, we address the…

The turnpike property in semilinear control

D. Pighin The turnpike property in semilinear control ESAIM Control Optim. Calc. Var., Vol. 26 (2021), pp. 1-48 Abstract.An exponential turnpike property for a semilinear control problem is proved. The…

The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms

M. Gugat, M. Schuster, E. Zuazua. The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-Smooth Tracking Terms, in "Stabilization of Distributed Parameter Systems: Design Methods and Applications". Grigory…

Large-time asymptotics in deep learning

deep learning, Neural ODEs, optimal control, Residual Neural Networks, Supervised Learning, turnpike property

Esteve C., Geshkovski B., Pighin D., Zuazua E. Large-time asymptotics in deep learning (2021). hal-02912516 Abstract. It is by now well-known that practical deep supervised learning may roughly be cast as…

Multiplicity of solutions for fractional q(.)-Laplacian equations

Abita Rahmoune, Umberto Biccari. Multiplicity of solutions for fractional -Laplacian equations. (2021) Abstract. In this paper, we deal with the following elliptic type problem where is a measurable function and is…

Multilevel Selective Harmonic Modulation via Optimal Control

Deyviss Jesús Oroya-Villalta, Carlos Esteve-Yagüe Umberto Biccari. Multilevel Selective Harmonic Modulation via Optimal Control. (2021) Abstract. We consider the Selective Harmonic Modulation (SHM) problem, consisting in the design of a staircase…

Local null controllability of a model system for strong interaction between internal solitary waves

Jon Asier Bárcena-Petisco, Sergio Guerrero and Ademir F. Pazoto. Local null controllability of a model system for strong interaction between internal solitary waves. Commun. Contemp. Math. (2021) https://doi.org/10.1142/S0219199721500036 Abstract. In…

Control and Deep Learning: Some connections

B. Geshkovski, E. Zuazua. Control and Deep Learning: Some connections (2021) This note is an extended abstract for a talk given by the second author during the workshop ”Challenges in…

Internal control for a non-local Schrödinger equation involving the fractional Laplace operator

U. Biccari Internal control for a non-local Schrödinger equation involving the fractional Laplace operator (2021) Abstract: We analyze the interior controllability problem for a nonlocal Schr\"odinger equation involving the fractional…

Nonnegative control of finite-dimensional linear systems

Dirac impulse, Minimal time, Nonnegative control

Lohéac J., Trélat E., Zuazua E. Nonnegative control of finite-dimensional linear systems. Ann. I. H. Poincare-An., Vol. 38, No. 2, pp. 301-346. (2021) DOI: https://doi.org/10.1016/j.anihpc.2020.07.004 Abstract. We consider the controllability…

Reachable subspaces, control regions and heat equations with memory

control regions, Controlled heat equations with memory, reachable subspaces

G. Wang, Y. Zhang, E. Zuazua. Reachable subspaces, control regions and heat equations with memory. (2021) Abstract. We study the controlled heat equations with analytic memory from two perspectives: reachable…

Rotor imbalance suppression by optimal control

M. Gnuffi, D. Pighin, N. Sakamoto Rotor imbalance suppression by optimal control (2021) Abstract. An imbalanced rotor is considered. A system of moving balancing masses is given. We determine the…

Analysis and numerics solvability of backward-forward conservation laws

Backward-forward method, Conservation Laws, Identification problems, Non-smooth optimization problem, Wave-front tracking algorithm, Weak-entropy solutions

Thibault Liard, Enrique Zuazua. Analysis and numerics solvability of backward-forward conservation laws. (2020) Abstract. In this paper, we study the problem of initial data identification for the one-dimensional Burgers equation.…

The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes

Hamilton-Jacobi equation, inverse design problem, obstacle problems, semiconcave envelopes

Esteve C., Zuazua E.. The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes SIAM J. Math. Anal., Vol. 52, No. 6, pp. 5627–5657 (2020). https://doi.org/10.1137/20M1330130 Abstract. We study the inverse…

Null-controllability of perturbed porous medium gas flow

degenerate parabolic equation, null controllability, porous medium equation, thin-ﬁlm equation

B. Geshkovski,Null-controllability of perturbed porous medium gas flow. ESAIM:COCV, vol. 26, No. 85 (2020). DOI: 10.1051/cocv/2020009 Abstract: In this work, we investigate the null-controllability of a nonlinear degenerate parabolic equation,…

Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations

Constraints, Controllability, Mathematical biology, Reaction-diffusion

Ruiz-Balet D., Zuazua E.. Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations. J. Math. Pures Appl, vol. 143, pp. 345-375 (2020) https://doi.org/10.1016/j.matpur.2020.08.006 Abstract. Dynamic phenomena in social and…

Sparse source identification of linear diffusion–advection equations by adjoint methods

Adjoint problem, Diffusion–advection equation, Inverse problems, optimal control, Optimization

Monge A., Zuazua E. Sparse source identification of linear diffusion–advection equations by adjoint methods. Syst. Control. Lett, vol. 145 (2020). DOI: https://doi.org/10.1016/j.sysconle.2020.104801 Abstract: We present an algorithm for the time-inversion…

The turnpike with lack of observability

Pighin D., Sakamoto N. The turnpike with lack of observability (2020) Abstract: We obtain turnpike results for optimal control problems with lack of stabilizability in the state equation and/or detectability in…

Controllability of a Class of Infinite Dimensional Systems with Age Structure

admisible control operator, age structure, infinite dimensional linear system, null controllability, population dynamics

Maity D., Tucsnak M., Zuazua E. Controllability of a Class of Infinite Dimensional Systems with Age Structure. Control Cybern. Vol. 48 (2020), No. 2, pp. 231-260 hal-01964612v2 Abstract: Given a…

Shape turnpike for linear parabolic PDE models

Direct methods, Optimal shape design, Parabolic equation, Strict dissipativity, Turnpike

Lance G., Trélat E., Zuazua E. Shape turnpike for linear parabolic PDE models Syst. Control. Lett. Vol. 142 (2020). DOI: 10.1016/j.sysconle.2020.104733 Abstract: We introduce and study the turnpike property for…

A stochastic approach to the synchronization of coupled oscillators

coupled oscillators, gradient descent, Kuramoto model, optimal control, random batch method, synchronization

Umberto Biccari, Enrique Zuazua. A stochastic approach to the synchronization of coupled oscillators. Frontiers in Energy Research, section Smart Grids. Front. Energy Res. Vol. 8 (2020). DOI: 10.3389/fenrg.2020.00115 Abstract. This paper…

Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditions

finite dimensional, linear control system, probabilistic

J.-C. Cortes, A. Navarro-Quiles, J.-V. Romero, M.-D. Rosello, E. Zuazua. Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditions. J. Franklin I. (2020)…

Turnpike in optimal shape design

Direct methods, heat equation, Optimal shape design, Strict dissipativity, Turnpike

G. Lance, E. Trélat, E. Zuazua Turnpike in optimal shape design IFAC-PapersOnline, Vol. 52, No. 16 (2019), pp. 496-501, ISSN: 24058963, DOI: 10.1137/17M1119160 Abstract: We investigate the turnpike problem in…

Stochastic optimization methods for the simultaneous control of parameter-dependent systems

Umberto Biccari, Ana Navarro-Quiles, Enrique Zuazua. Stochastic optimization methods for the simultaneous control of parameter-dependent systems (2020) Abstract. We address the application of stochastic optimization methods for the simultaneous control of…

Asymptotic behavior and control of a “guidance by repulsion” model

Asymptotic stability, Collective behavior, Guidance by repulsion, Herding, optimal control

Dongnam Ko, E. Zuazua, Asymptotic behavior and control of a "guidance by repulsion" model. Math Models Methods Appl. Sci. Vol. 30, No. 04, pp. 765-804 (2020).DOI:10.1142/S0218202520400047 Abstract. We model and…

Stochastic persistency of nematic alignment state for the Justh-Krishnaprasad model with additive white noises

Alignment, emergence, Justh–Krishnaprasad model, nematic alignment, stochastic noises

Seung-Yeal Ha, Dongnam Ko, Woojoo Shim, Hui Yu, . Stochastic persistency of nematic alignment state for the Justh-Krishnaprasad model with additive white noises. Math Models Methods Appl. Sci. Vol. 30,…

The turnpike property in nonlinear optimal control – A geometric approach

dynamical system theory, general dynamical systems, geometric approach, nonlinear optimal control, optimal control problems, turnpike property, turnpike-like property

N. Sakamoto, D. Pighin, E. Zuazua The turnpike property in nonlinear optimal control - A geometric approach. IEEE 58th Conference on Decision and Control (CDC) (2020). DOI: 10.1109/CDC40024.2019.9028863 Abstract: This paper…

Controllability of the one-dimensional fractional heat equation under positivity constraints

U. Biccari, M. Warna, E. Zuazua Internal observability for coupled systems of linear partial differential equations. Commun. Pure Appl. Anal., Vol 19. No. 4 (2019), pp. 1949-1978. DOI: 10.3934/cppaa.2020086

Cost of null controllability for parabolic equations with vanishing diffusivity and a transport term

heat equation, singular limits, spectral decomposition, transport equation, uniform controllability

Bárcena-Petisco J.A., Cost of null controllability for parabolic equations with vanishing diffusivity and a transport term (2020). HAL Id: hal-02455632 Abstract. In this paper we consider the heat equation with…

A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diﬀusive models

I. Mazari, D. Ruiz-Balet. A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diﬀusive models (2020) Abstract. Following the recent works [9, 17,…

Asymptotic behavior of scalar convection-diffusion equations

Enrique Zuazua. Asymptotic behavior of scalar convection-diffusion equations (2020) Abstract. In these lecture notes, we address the problem of large-time asymptotic behaviour of the solutions to scalar convection-diffusion equations set in…

A PDE-ODE model for traffic control with autonomous vehicles

Thibault Liard, Raphael Stern, Maria Laura Delle Monache. A PDE-ODE model for traffic control with autonomous vehicles. (2020) Abstract. We introduce a coupled PDE-ODEs model to describe mixed traffic with…

Emergent collective behaviors of stochastic kuramoto oscillators

Kuramoto model, mean-field limit, multiplicative noise, random environment, synchronization

Seung-Yeal Ha, Dongnam Ko, Chanho Min, Xiongtao Zhang. Emergent collective behaviors of stochastic kuramoto oscillators. Vol. 25, No. 3, pp. 1059-1081 (2020) DOI: 10.3934/dcdsb.2019208 Abstract. We study the collective dynamics…

Flocking Behaviors of a Cucker-Smale Ensemble in a Cylindrical Domain

aggregation, Alignment, Cucker--Smale model, flocking, specular reflection

Hyeong-Ohk Bae, Seung-Yeal Ha, Jeongho Kim, Dongnam Ko, Sung-Ik Sohn. Flocking Behaviors of a Cucker--Smale Ensemble in a Cylindrical Domain. SIAM J. Math. Anal., 51(3), pp. 2390–2424 (2019). DOI: https://doi.org/10.1137/18M122025X…

Null-controllability properties of a fractional wave equation with a memory term

fractional wave equation, memory term, null controllability

U. Biccari, M. Warma Null-controllability properties of a fractional wave equation with a memory term. Evol. Eq. Control The., Vol. 9, No. 2 (2020), pp. 399-430 Abstract: We study the…

Existence and cost of boundary controls for a degenerate/singular parabolic equation

Umberto Biccari, Víctor Hernández-Santamaría, Judith Vancostenoble. Existence and cost of boundary controls for a degenerate/singular parabolic equation (2020). Abstract. In this paper, we consider the following degenerate/singular parabolic equation ,…

Propagation of one and two-dimensional discrete waves under finite difference approximation

U. Biccari, A. Marica, E. Zuazua Propagation of one and two/dimensional discrete waves under finite difference approximation, Found. Comput. Math., Vol. 20 (2020), pp. 1401-1438. DOI: 10.1007/s10208-020-09445-0 Abstract: We analyze…

Output controllability in a long-time horizon

Averaged control, Controlled invariant subspace, Linear optimal control, Open-loop control systems, Output controllability

Martin Lazar, Jerôme Lohéac. Output controllability in a long-time horizon. Automatica, Vol. 113 (2020). DOI: 10.1016/j.automatica.2019.108762 Abstract. In this article we consider a linear finite dimensional system. Our aim is…

A controlled multiscale model for traffic regulation via autonomous vehicles

T. Liard, . A controlled multiscale model for traffic regulation via autonomous vehicles. (2019) Abstract. Autonomous vehicles ($AV$s) allow new ways of regulating the traffic flow on road networks. Most…

On entropic solutions to conservation laws coupled with moving bottlenecks

T. Liard, Benedetto Piccoli. On entropic solutions to conservation laws coupled with moving bottlenecks. (2019) Abstract. Moving bottlenecks in road traffic represent an interesting mathematical problem, which can be modeled…

Optimal driving strategies for traffic control with autonomous vehicles

T. Liard, Raphael Stern, Maria Laura Delle Monache. Optimal driving strategies for traffic control with autonomous vehicles. (2019) Abstract. This article considers the possibility of using a small number of…

Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem

decay rates, nonlocal diffusion

C. Esteve, J.D. Rossi, A. San Antolín. Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem. BOUND VALUE PROBL (2014), pp. 109. DOI: 10.1186/1687-2770-2014-109 Abstract. We obtain…

Inverse design for the one-dimensional Burgers equation

T. Liard, E. Zuazua. Inverse design for the one-dimensional Burgers equation. (2019) Abstract. In this paper, we study the problem of inverse design for the one-dimensional Burgers equation. This problem…

Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity

C. Esteve, Ph Souplet. Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity, NONLINEARITY, Vol. 31, No. 11 (2018). DOI: 10.1088/1361-6544 Abstract. We consider a well-known model for…

The evolution problem associated with eigenvalues of the Hessian

P. Blanc, C. Esteve, J. D. Rossi. The evolution problem associated with eigenvalues of the Hessian. J. London Math. Soc. (2020). https://doi.org/10.1112/jlms.12363 Abstract. In this paper we study the evolution…

Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature

C. Esteve Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvatureJ MATH PURE APPL, Vol 137 (2020) pp. 143-177, DOI: 10.1016/j.matpur.2019.12.006 Abstract. We consider…

No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem

C. Esteve, Ph. Souplet, No touchdown at points of small permittivity and nontrivial touchdown sets for the MEMS problem Adv. Differential Equ. Vol. 24, No. 7/8 (2019), pp. 465-500 https://projecteuclid.org/euclid.ade/1556762456…

Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation

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