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…
View More Differentiability with respect to the initial condition for Hamilton-Jacobi equationsCategory: Enrique Zuazua
Author is Enrique Zuazua
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 (2021) Abstract. In this article, we explore the effects…
View More Interpolation and approximation via Momentum ResNets and Neural ODEsControl 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…
View More Control of certain parabolic models from biology and social sciencesControl and Numerical approximation of Fractional Diffusion Equations
Umberto Biccari, Mahamadi Warma, Enrique Zuazua. Control and Numerical approximation of Fractional Diffusion Equations (2021) Handb. Numer. Anal. Abstract. The aim of this work is to…
View More Control and Numerical approximation of Fractional Diffusion EquationsSidewise control of 1-d waves
Yesim Sarac, Enrique Zuazua. Sidewise control of 1-d waves. (2021) Abstract. We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control…
View More Sidewise control of 1-d wavesA framework for randomized time-splitting in linear-quadratic optimal control
Daniël Veldman, Enrique Zuazua. A framework for randomized time-splitting in linear-quadratic optimal control (2021) Abstract. Inspired by the successes of stochastic algorithms in the training of…
View More A framework for randomized time-splitting in linear-quadratic optimal controlThe 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 (2021) Numer Math (Heidelb) Abstract. We consider the Vlasov-Fokker-Planck equation…
View More The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing TermAveraged 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. Abstract. This paper deals with the averaged…
View More Averaged dynamics and control for heat equations with random diffusionFlow decomposition for heat equations with memory
G. Wang, Y. Zhang, E. Zuazua. Flow decomposition for heat equations with memory (2021) J. Math. Pures Appl. Abstract. We build up a decomposition for…
View More Flow decomposition for heat equations with memorySpecial 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…
View More Special issue in the honor of Enrique Zuazua’s 60th birthdayMultilevel 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…
View More Multilevel control by dualityModel predictive control with random batch methods for a guiding problem
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,…
View More Model predictive control with random batch methods for a guiding problemClassical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems
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. Abstract.…
View More Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systemsSlow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems
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…
View More Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problemsOptimal actuator design via Brunovsky’s normal form
B. Geshkovski, E. Zuazua, Optimal actuator design via Brunovsky’s normal form (2021) Abstract: In this paper, by using the Brunovsky normal form, we provide a…
View More Optimal actuator design via Brunovsky’s normal formThe turnpike property in nonlinear optimal control – A geometric approach
N. Sakamoto, E. Zuazua. The turnpike property in nonlinear optimal control – A geometric approach. (2021) Automatica. Abstract: This paper presents, using dynamical system theory,…
View More The turnpike property in nonlinear optimal control – A geometric approachInitial data identification for the one-dimensional Burgers equation
Thibault Liard, Enrique Zuazua. Initial data identification for the one-dimensional Burgers equation. (2021). IEEE T Automat. Contr. DOI: 10.1109/TAC.2021.3096921 Abstract. In this paper, we study…
View More Initial data identification for the one-dimensional Burgers equationA 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…
View More A quantitative analysis of Koopman operator methods for system identification and predictionsControl of Hyperbolic and Parabolic Equations on Networks and Singular limits
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…
View More Control of Hyperbolic and Parabolic Equations on Networks and Singular limitsControllability 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…
View More Controllability of one-dimensional viscous free boundary flowsThe turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation
C. Esteve, H. Kouhkouh, D. Pighin, E. Zuazua. The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation Abstract: In this work, we analyze the…
View More The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equationConstrained control of gene-flow models
Mazari I., Ruiz-Balet D., Zuazua E.. Constrained control of gene-flow models. (2021) ⟨hal-02373668⟩ Abstract. In ecology and population dynamics, gene-flow refers to the transfer of…
View More Constrained control of gene-flow modelsNeural ODE Control for Classification, Approximation and Transport
Ruiz-Balet D., Zuazua E. Neural ODE Control for Classification, Approximation and Transport (2021) Abstract. We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical…
View More Neural ODE Control for Classification, Approximation and TransportThe 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:…
View More The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking TermsLarge-time asymptotics in deep learning
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…
View More Large-time asymptotics in deep learningControl 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…
View More Control and Deep Learning: Some connectionsNonnegative control of finite-dimensional linear systems
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…
View More Nonnegative control of finite-dimensional linear systemsReachable subspaces, control regions and heat equations with memory
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…
View More Reachable subspaces, control regions and heat equations with memoryAnalysis and numerics solvability of backward-forward conservation laws
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…
View More Analysis and numerics solvability of backward-forward conservation lawsTurnpike in Lipschitz-nonlinear optimal control
Esteve C., Geshkovski G., Pighin D., Zuazua E. . Turnpike in Lipschitz-nonlinear optimal control (2020) Abstract. We present a new proof of the turnpike property…
View More Turnpike in Lipschitz-nonlinear optimal controlThe Inverse Problem for Hamilton-Jacobi equations and 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…
View More The Inverse Problem for Hamilton-Jacobi equations and Semiconcave EnvelopesControl under constraints for multi-dimensional reaction-diffusion monostable and bistable equations
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.…
View More Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equationsSparse source identification of linear diffusion–advection equations by adjoint methods
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…
View More Sparse source identification of linear diffusion–advection equations by adjoint methodsControllability of a Class of Infinite Dimensional Systems with Age Structure
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.…
View More Controllability of a Class of Infinite Dimensional Systems with Age StructureShape turnpike for linear parabolic PDE models
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…
View More Shape turnpike for linear parabolic PDE modelsA stochastic approach to the synchronization of coupled oscillators
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).…
View More A stochastic approach to the synchronization of coupled oscillatorsFull probabilistic solution of a infinite dimensional linear control system with random initial and final conditions
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…
View More Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditionsTurnpike in optimal shape design
G. Lance, E. Trélat, E. Zuazua Turnpike in optimal shape design IFAC-PAPERSONLINE. (ISSN: 24058963). 52(16): 496-501. DOI: 10.1137/17M1119160 Abstract: We investigate the turnpike problem in…
View More Turnpike in optimal shape designStochastic 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…
View More Stochastic optimization methods for the simultaneous control of parameter-dependent systemsAsymptotic behavior and control of a “guidance by repulsion” model
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…
View More Asymptotic behavior and control of a “guidance by repulsion” modelThe turnpike property in nonlinear optimal control – A geometric approach
N. Sakamoto, D. Pighin, E. Zuazua The turnpike property in nonlinear optimal control – A geometric approach. IEEE 58th Conference on Decision and Control (CDC)…
View More The turnpike property in nonlinear optimal control – A geometric approachAsymptotic 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…
View More Asymptotic behavior of scalar convection-diffusion equationsPropagation 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 (2020). DOI: 10.1007/s10208-020-09445-0 Abstract: We analyze…
View More Propagation of one and two-dimensional discrete waves under finite difference approximationInverse 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…
View More Inverse design for the one-dimensional Burgers equationModel reduction of converter-dominated power systems by Singular Perturbation Theory
U. Biccari, N. Sakamoto, E. Unamuno, D. Madariaga, E. Zuazua, J.A. Barrena. Model reduction of converter-dominated power systems by Singular Perturbation Theory Abstract: The increasing integration of power electronic devices is driving the development of more…
View More Model reduction of converter-dominated power systems by Singular Perturbation TheoryAdjoint computational methods for 2D inverse design of linear transport equations on unstructured grids
M. Morales-Hernández, E. Zuazua Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids Comp. Appl. Math. Vol. 38, No. 168 (2019)…
View More Adjoint computational methods for 2D inverse design of linear transport equations on unstructured gridsSpectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions
Y. Privat, E. Trélat & E. Zuazua. Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions. CALC VAR PARTIAL DIF. Springer Verlag, Vol.…
View More Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctionsControllability 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
View More Controllability of the one-dimensional fractional heat equation under positivity constraintsDynamics and control for multi-agent networked systems: a finite difference approach
U. Biccari, D. Ko, E. Zuazua Dynamics and control for multi-agent networked systems: a finite difference approach. Math. Models Methods Appl. Sci., Vol. 29, No.…
View More Dynamics and control for multi-agent networked systems: a finite difference approachPhase portrait control for 1D monostable and bistable reaction-diffusion equations
Pouchol C., Trélat E., Zuazua E. Phase portrait control for 1D monostable and bistable reaction-diffusion equations. Nonlinearity, Vol. 32, No. 3 (2019). DOI: 10.1088/1361-6544/aaf07e Abstract:…
View More Phase portrait control for 1D monostable and bistable reaction-diffusion equationsA parabolic approach to the control of opinion spreading
D. Ruiz-Balet, E. Zuazua A parabolic approach to the control of opinion spreading. In: Berezovski A., Soomere T. (eds) Applied Wave Mathematics II. Mathematics of…
View More A parabolic approach to the control of opinion spreadingInternal observability for coupled systems of linear partial differential equations
Lissy, P., Zuazua, E. Internal observability for coupled systems of linear partial differential equations , SIAM J. Control Optim., Vol. 57, No. 2 (2019), pp.…
View More Internal observability for coupled systems of linear partial differential equationsA Two-Dimensional “Flea on the Elephant” Phenomenon and its Numerical Visualization
Bianchini, R., Gosse, L., Zuazua, E. A two-dimensional “flea on the elephant” phenomenon and its numerical visualization , Multiscale Model. Simul., Vol. 17, No. 1…
View More A Two-Dimensional “Flea on the Elephant” Phenomenon and its Numerical VisualizationGreedy optimal control for elliptic problems and its application to turnpike problems
Hernández-Santamaría V., Lazar M., Zuazua E. Greedy optimal control for elliptic problems and itsapplication to turnpike problemsNUMER MATH. Vol. 141, No. 2, pp.455-493 (2019) DOI:…
View More Greedy optimal control for elliptic problems and its application to turnpike problemsTurnpike in optimal shape design for heat equation
G. Lance, E. Trélat, E. Zuazua Turnpike in optimal shape design for heat equation Abstract: After a short presentation of the turnpike’s problem in optimal…
View More Turnpike in optimal shape design for heat equationControllability of shadow reaction-diffusion systems
Hernández-Santamaría V., E. Zuazua. Controllability of shadow reaction-diffusion systems. J Differ Equations, Vol. 268, No. 7, pp. 3781-3818 (2020). DOI: 10.1016/j.jde.2019.10.012 Abstract: We study the…
View More Controllability of shadow reaction-diffusion systemsControllability and Positivity Constraints in Population Dynamics with Age Structuring and Diffusion
D. Maity, M. Tucsnak, E. Zuazua. Controllability and Positivity Constraints in Population Dynamics with Age Structuring and Diffusion, J MATH PURE APPL. Vol. 129 (2019),…
View More Controllability and Positivity Constraints in Population Dynamics with Age Structuring and DiffusionDecay rates for elastic-thermoelastic star-shaped networks
Han Z., Zuazua E. Decay rates for elastic-thermoelastic star-shaped networks Network and Heterogeneous Media, NETW HETEROG MEDIA, Vol. 12, No. 3 (2017), pp. 461-488. DOI:…
View More Decay rates for elastic-thermoelastic star-shaped networksControllability under positivity constraints of multi-d wave equations
Pighin, D., Zuazua, E. Controllability under positivity constraints of multi-d wave equations , Trends in Control Theory and Partial Differential Equations., Vol 32 (2019). DOI:…
View More Controllability under positivity constraints of multi-d wave equationsSteady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces
Trélat E., Zhang C., and Zuazua E. Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces SIAM J. Control Optim., Vol.…
View More Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spacesOptimal shape design for 2D heat equations in large time
Trélat E., Zhang C., Zuazua E. Optimal shape design for 2D heat equations in large time J. Appl. Funct. Anal., Vol. 3 (2018), pp. 255-269.…
View More Optimal shape design for 2D heat equations in large timeMinimal controllability time for finite-dimensional control systems under state constraints
Lohéac J., Trélat E., Zuazua, E. Minimal controllability time for finite-dimensional control systems under state constraints Automática, Vol. 96 (2018), pp. 380-392. DOI: 10.1016/j.automatica.2018.07.010 Abstract:…
View More Minimal controllability time for finite-dimensional control systems under state constraintsInternal Controllability for Parabolic Systems Involving Analytic Non-local Terms
Lissy P, and Zuazua E.Internal Controllability for Parabolic Systems Involving Analytic Non-local TermsCHINESE ANN MATH B. Vol. 39, No. 2 (2018), pp. 281-296 DOI: 10.1007/s11401-018-1064-6…
View More Internal Controllability for Parabolic Systems Involving Analytic Non-local TermsAllee optimal control of a system in ecology
Trélat E., Zhu J., Zuazua, E. Allee optimal control of a system in ecology , Mathematical Models and Methods in Applied Sciences DOI: 10.1142/S021820251840002X Abstract:…
View More Allee optimal control of a system in ecologyPreface: A tribute to professor Eduardo Casas on his 60th birthday
Fernández L.A., Mateos M., Pola C., Tröltzsch F., Zuazua E. Preface: A tribute to professor Eduardo Casas on his 60th birthday MATH CONTROL RELAT F.…
View More Preface: A tribute to professor Eduardo Casas on his 60th birthdayControllability under positivity constraints of semilinear heat equations
Pighin, D., Zuazua, E. Controllability under positivity constraints of semilinear heat equations MATH CONTROL RELAT F., Vol. 8, No. 3-4 (2018). DOI: 10.3934/mcrf.2018041 Abstract: In…
View More Controllability under positivity constraints of semilinear heat equationsGreedy optimal control for elliptic problems and its application to turnpike problems
Hernández-Santamaría V., Lazar M., Zuazua E. , Greedy optimal control for elliptic problems and its application to turnpike problems. Numer Math. Vol. 141, No. 2…
View More Greedy optimal control for elliptic problems and its application to turnpike problemsLocal regularity for fractional heat equations
U. Biccari, M. Warma, E. Zuazua Local regularity for fractional heat equations<, Recent Advances in PDEs: Analysis, Numerics and Control, SEMA SIMAI Springer Series, Vol.…
View More Local regularity for fractional heat equationsControllability of Evolution Equations with Memory
Felipe W. Chaves-Silva, Xu Zhang, and Enrique Zuazua Controllability of Evolution Equations with Memory. SIAM J. Control Optim., 55(4), 2437–2459. (23 pages) DOI: 10.1137/151004239 Abstract: This…
View More Controllability of Evolution Equations with MemoryNull controllability for wave equations with memory
Lu Q., Zhang X., Zuazua E. Null controllability for wave equations with memory Journal de Mathématiques Pures et Appliquées DOI: 10.1016/j.matpur.2017.05.001 Abstract: We study the…
View More Null controllability for wave equations with memoryFiltered gradient algorithms for inverse design problems of one-dimensional Burgers equation
L. Gosse, E. Zuazua. Filtered gradient algorithms for inverse design problems of one-dimensional Burgers equation. Innovative Algorithms and Analysis,Gosse, Laurent, Natalini, Roberto (Eds.), Springer INdAM…
View More Filtered gradient algorithms for inverse design problems of one-dimensional Burgers equationAveraged controllability of parameter dependent conservative semigroups
Lohéac J., Zuazua E. Averaged controllability of parameter dependent conservative semigroups Journal of Differential Equations, 262 (3) (2017), 1540–1574 DOI: 10.1016/j.jde.2016.10.017 Abstract: We consider the…
View More Averaged controllability of parameter dependent conservative semigroups
Minimal controllability time for the heat equation under unilateral state or control constraints
Lohéac J., Trélat E., Zuazua E. Minimal controllability time for the heat equation under unilateral state or control constraints . Mathematical Models and Methods in Applied…
View More Minimal controllability time for the heat equation under unilateral state or control constraintsLocal elliptic regularity for the Dirichlet fractional Laplacian
U. Biccari, M. Warma, E. Zuazua Local elliptic regularity for the Dirichlet fractional Laplacian Advanced Nonlinear Studies, Vol. 17, Nr. 2 (2017), pp. 387-409. DOI:…
View More Local elliptic regularity for the Dirichlet fractional LaplacianAddendum: Local elliptic regularity for the Dirichlet fractional Laplacian
U. Biccari, M. Warma, E. Zuazua Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian Adv. Nonlinear Stud., Vol. 17, Nr. 4 (2017), pp. 837-839.…
View More Addendum: Local elliptic regularity for the Dirichlet fractional LaplacianLarge time control and turnpike properties for wave equations
Zuazua E. Large time control and turnpike properties for wave equations ANNU REV CONTROL. Vol. 40 (2017), pp. 199-210 DOI: 10.1016/j.arcontrol.2017.04.002 Abstract: In the last…
View More Large time control and turnpike properties for wave equationsActuator design for parabolic distributed parameter systems with the moment method
Privat Y., Trélat E., Zuazua E. Actuator design for parabolic distributed parameter systems with the moment method SIAM J CONTROL OPTIM. Vol. 55, No. 2…
View More Actuator design for parabolic distributed parameter systems with the moment methodOptimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains
Privat Y., Trélat E., Zuazua E. Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains J EUR MATH SOC. Vol. 18,…
View More Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains
Dispersion for 1-D Schrödinger and wave equations with BV coefficients
Beli C. N., Ignat L. I., Zuazua E. Dispersion for 1-D Schrödinger and wave equations with BV coefficients ANN I H POINCARE-AN. Vol. No. 33…
View More Dispersion for 1-D Schrödinger and wave equations with BV coefficients
Numerical aspects of sonic-boom minimization
Allahverdi N., Pozo A., Zuazua E. Numerical aspects of sonic-boom minimization COMMUN CONTEMP MATH. Vol. No. 658 (2016), pp. 267 – 279. DOI: 10.1090/conm/658/13133 Abstract:…
View More Numerical aspects of sonic-boom minimizationNumerical meshes ensuring uniform observability of one-dimensional waves: construction and analysis
Ervedoza S., Marica A., Zuazua E. Numerical meshes ensuring uniform observability of one-dimensional waves: construction and analysis IMA J NUMER ANAL. Vol. 36, No. 2…
View More Numerical meshes ensuring uniform observability of one-dimensional waves: construction and analysis
Averaged controllability for random evolution Partial Differential Equations
Lu Q., Zuazua E. Averaged controllability for random evolution Partial Differential Equations J MATH PURE APPL. Vol. 105, No. 3 (2016)., pp. 367–414. DOI: 10.1016/j.matpur.2015.11.004…
View More Averaged controllability for random evolution Partial Differential Equations
Numerical aspects of large-time optimal control of Burgers equation
Allahverdi N., Pozo A., Zuazua E. Numerical aspects of large-time optimal control of Burgers equation ESAIM-MATH MODEL NUM. Vol. 50. No. 5 (2016). DOI: 10.1051/m2an/2015076…
View More Numerical aspects of large-time optimal control of Burgers equationRemarks on Long Time Versus Steady State Optimal Control
Porretta A., Zuazua E. Remarks on Long Time Versus Steady State Optimal Control Mathematical Paradigms of Climate Science -Springer INdAM Series, Vol. 15 (2016), pp…
View More Remarks on Long Time Versus Steady State Optimal ControlExact penalization of terminal constraints for optimal control problems
Gugat M., Zuazua E. Exact penalization of terminal constraints for optimal control problems >OPTIM CONTR APPL MET., Vol. 37, No. 6 (2016), pp. 1329–1354, DOI:…
View More Exact penalization of terminal constraints for optimal control problems
Randomised observation, control and stabilization of waves
Privat Y., Trélat E., Zuazua E. Randomised observation, control and stabilization of waves J Appl Math Mech Z Angew Math Mech. Vol. 96, No. 5…
View More Randomised observation, control and stabilization of wavesOn the lack of controllability of fractional in time ODE and PDE
Lu Q., Zuazua E. On the lack of controllability of fractional in time ODE and PDE MATH CONTROL SIGNAL. Vol. No. 2 (2016), pp. 28:10…
View More On the lack of controllability of fractional in time ODE and PDE
Optimal Neumann control for the 1D wave equation
Gugat M., Trélat E., Zuazua E. Optimal Neumann control for the 1D wave equation: Finite horizon, infinite horizon, boundary tracking terms and the turnpike property…
View More Optimal Neumann control for the 1D wave equation
Optimal strategies for driving a mobile agent in a “guidance by repulsion” model
Escobedo R., Ibañez A., Zuazua E Optimal strategies for driving a mobile agent in a “guidance by repulsion” model COMMUN NONLINEAR SCI., Vol.39 (2016), pp.…
View More Optimal strategies for driving a mobile agent in a “guidance by repulsion” model
Stable observation of additive superpositions of Partial Differential Equations
E. Zuazua. Stable observation of additive superpositions of Partial Differential Equations. Syst. Control. Lett. Vol.93 (2016), pp. 21–29, DOI: 10.1016/j.sysconle.2016.02.017 Abstract: We address the problem of…
View More Stable observation of additive superpositions of Partial Differential Equations
From averaged to simultaneous controllability
Lohéac J., Zuazua E. From averaged to simultaneous controllability Ann. Fac. Sci. Toulouse Math. Vol.25, No.4 (2016), pp. 785-828, DOI: 10.5802/afst.1511 Abstract: We consider a…
View More From averaged to simultaneous controllability
Null Controllability of Linear Heat and Wave Equations with Nonlocal Spatial Terms
Fernández-Cara E., Lu Q., Zuazua E. Null Controllability of Linear Heat and Wave Equations with Nonlocal Spatial Terms SIAM J. Control Optim. Vol. 54, No.4…
View More Null Controllability of Linear Heat and Wave Equations with Nonlocal Spatial TermsNull controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function
U. Biccari, E. Zuazua Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function J. Differential Equations,…
View More Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function
Decay rates for 1−d heat-wave planar networks
Han Z.-J., Zuazua E. Decay rates for 1−d heat-wave planar networks NETW HETEROG MEDIA. Vol. 11, No. 4 (2016), pp. 655–692,DOI: 10.3934/nhm.2016013 Abstract: The large…
View More Decay rates for 1−d heat-wave planar networks
Greedy controllability of finite dimensional linear systems
Lazar M., Zuazua E. Greedy controllability of finite dimensional linear systems Automatica, Vol.74 (2016), pp. 327-340 DOI: 10.1016/j.automatica.2016.08.010 Abstract: We analyse the problem of controllability…
View More Greedy controllability of finite dimensional linear systems
Norm saturating property of time optimal controls for wave-type equations
Lohéac. J, Zuazua E. Norm saturating property of time optimal controls for wave-type equations IFAC-PapersOnLine, Vol. 49, No.8 (2016), pp. 37-42. DOI: 10.1016/j.ifacol.2016.07.415 Abstract: We…
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Lipschitz dependence of the coefficients on the resolvent and greedy approximation for scalar elliptic problems
We analyze the inverse problem of identifying the diffusivity coefficient of a scalar elliptic equation as a function of the resolvent operator. We prove that, within the class of measurable coefficients, bounded above and below by positive constants, the resolvent determines the diffusivity in an unique manner…
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Numerical hypocoercivity for the Kolmogorov equation
We prove that a finite-difference centered approximation for the Kolmogorov equation in the whole space preserves the decay properties of continuous solutions as $ t \to \infty $, independently of the mesh-size parameters.
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