Dynamic Control and Numerics of Partial Differential Equations

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Publications

Averaged dynamics and control for heat equations with random diffusion

Author(s): Jon Asier Bárcena Petisco, Enrique Zuazua
Published in: Systems & Control Letters, 01676911, 2021, Page(s) 105055, ISSN 0167-6911
Publisher: Elsevier BV
DOI: 10.1016/j.sysconle.2021.105055

Applying the random variable transformation method to solve a class of random linear differential equation with discrete delay

Author(s): Tomás Caraballo, J.-C. Cortés, A. Navarro-Quiles
Published in: Applied Mathematics and Computation, 356, 2019, Page(s) 198-218, ISSN 0096-3003
Publisher: Elsevier BV
DOI: 10.1016/j.amc.2019.03.048

Turnpike in Lipschitz-nonlinear optimal control

Author(s): Carlos Esteve, B. Geshkovski, Dario Pighin, Enrique Zuazua
Published in: Nonlinearity, 09517715, 2022, Page(s) 1652-1701, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ac4e61

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

Author(s): Umberto Biccari, Mahamadi Warma, Enrique Zuazua
Published in: Communications on Pure & Applied Analysis, 19/4, 2020, Page(s) 1949-1978, ISSN 1534-0392
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/cpaa.2020086

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

Author(s): Daniël Veldman, Enrique Zuazua
Published in: Numerische Mathematik, 0029599X, 2022, Page(s) 495-549, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-022-01290-3

Slow decay and turnpike for infinite-horizon hyperbolic LQ problems

Author(s): Han, Zhong-Jie; Zuazua, Enrique
Published in: SIAM Journal on Control and Optimization, 03630129, 2022, Page(s) 2440-2468, ISSN 0363-0129
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.48550/arxiv.2108.10240

Numerical hypocoercivity for the Kolmogorov equation

Author(s): Alessio Porretta, Enrique Zuazua
Published in: Mathematics of Computation, 86/303, 2017, Page(s) 97-119, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3157

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

Author(s): Shi Jin, Yuhua Zhu, Enrique Zuazua
Published in: Numerische Mathematics, 0029599X, 2022, Page(s) 479-519, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-021-01257-w

On coupling kinetic and Schrödinger equations

Author(s): Avy Soffer, Minh-Binh Tran
Published in: Journal of Differential Equations, 265/5, 2018, Page(s) 2243-2279, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2018.04.031

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

Author(s): Jon Asier Bárcena-Petisco, Sergio Guerrero, Ademir F. Pazoto
Published in: Communications in Contemporary Mathematics, 2021, Page(s) 2150003, ISSN 0219-1997
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0219199721500036

Null-controllability of perturbed porous medium gas flow

Author(s): Borjan Geshkovski
Published in: ESAIM: Control, Optimisation and Calculus of Variations, 26, 2020, Page(s) 85, ISSN 1292-8119
Publisher: EDP Sciences
DOI: 10.1051/cocv/2020009

Existence and uniqueness of maximal strong solution of a 1D blood flow in a network of vessels

Author(s): Debayan Maity; Jean-Pierre Raymond; Arnab Roy
Published in: Nonlinear Analysis: Real World Applications, 14681218, 2022, Page(s) 103405, ISSN 1468-1218
Publisher: Elsevier BV
DOI: 10.1016/j.nonrwa.2021.103405

Sidewise control of 1-d waves.

Author(s): Yesim Sarac, Enrique Zuazua
Published in: Journal of Optimization Theory and Applications, 00223239, 2022, ISSN 0022-3239
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10957-021-01986-w

Quantitative Stability for Eigenvalues of Schrödinger Operator, Quantitative Bathtub Principle, and Application to the Turnpike Property for a Bilinear Optimal Control Problem

Author(s): Idriss Mazari; Domènec Ruiz-Balet
Published in: SIAM Journal on Mathematical Analysis, 00361410, 2022, Page(s) 3848-3883., ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1393121

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

Author(s): Domènec Ruiz-Balet, Enrique Zuazua
Published in: Journal de Mathématiques Pures et Appliquées, 143, 2020, Page(s) 345-375, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2020.08.006

Interpolation and approximation via Momentum ResNets and Neural ODEs

Author(s): Domènec Ruiz-Balet, Elisa Affili, Enrique Zuazua.
Published in: IEEE Control Systems Letters, 24751456, 2022, ISSN 2475-1456
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1016/j.sysconle.2022.105182

The Inverse Problem for Hamilton--Jacobi Equations and Semiconcave Envelopes

Author(s): Carlos Esteve, Enrique Zuazua
Published in: SIAM Journal on Mathematical Analysis, 52/6, 2020, Page(s) 5627-5657, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1330130

Optimal distributed control of linear parabolic equations by spectral decomposition

Author(s): Martin Lazar; Cesare Molinari
Published in: Optimal Control Applications and Methods, 10991514, 2021, Page(s) 891-926, ISSN 1099-1514
Publisher: John Wiley & Sons Ltd
DOI: 10.1002/oca.2708

Propagation of One- and Two-Dimensional Discrete Waves Under Finite Difference Approximation

Author(s): Umberto Biccari, Aurora Marica, Enrique Zuazua
Published in: Foundations of Computational Mathematics, 20/6, 2020, Page(s) 1401-1438, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-020-09445-0

A multiscale model for traffic regulation via autonomous vehicles

Author(s): Mauro Garavello, Paola Goatin, Thibault Liard, Benedetto Piccoli
Published in: Journal of Differential Equations, 269/7, 2020, Page(s) 6088-6124, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2020.04.031

Greedy algorithm for parameter dependent operator Lyapunov equations

Author(s): Martin Lazar; Jerome Weston
Published in: Systems & Control Letters, 01676911, 2021, Page(s) 104968, ISSN 0167-6911
Publisher: Elsevier BV
DOI: 10.1016/j.sysconle.2021.104968

Steady-State and Periodic Exponential Turnpike Property for Optimal Control Problems in Hilbert Spaces

Author(s): Emmanuel Trélat, Can Zhang, Enrique Zuazua
Published in: SIAM Journal on Control and Optimization, 56/2, 2018, Page(s) 1222-1252, ISSN 0363-0129
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/16M1097638

Local Elliptic Regularity for the Dirichlet Fractional Laplacian

Author(s): Umberto Biccari, Mahamadi Warma, Enrique Zuazua
Published in: Advanced Nonlinear Studies, 17/2, 2017, ISSN 1536-1365
Publisher: UTHSCSA Press
DOI: 10.1515/ans-2017-0014

Actuator Design for Parabolic Distributed Parameter Systems with the Moment Method

Author(s): Yannick Privat, Emmanuel Trélat, Enrique Zuazua
Published in: SIAM Journal on Control and Optimization, 55/2, 2017, Page(s) 1128-1152, ISSN 0363-0129
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/16M1058418

Minimal controllability time for the heat equation under unilateral state or control constraints

Author(s): Jérôme Lohéac, Emmanuel Trélat, Enrique Zuazua
Published in: Mathematical Models and Methods in Applied Sciences, 27/09, 2017, Page(s) 1587-1644, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/S0218202517500270

Decay rates for elastic-thermoelastic star-shaped networks

Author(s): Zhong-Jie Han, Enrique Zuazua
Published in: Networks and Heterogeneous Media, 12/3, 2017, Page(s) 461-488, ISSN 1556-1801
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/nhm.2017020

Controllability of Evolution Equations with Memory

Author(s): Felipe W. Chaves-Silva, Xu Zhang, Enrique Zuazua
Published in: SIAM Journal on Control and Optimization, 55/4, 2017, Page(s) 2437-2459, ISSN 0363-0129
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/151004239

Averaged controllability of parameter dependent conservative semigroups

Author(s): Jérôme Lohéac, Enrique Zuazua
Published in: Journal of Differential Equations, 262/3, 2017, Page(s) 1540-1574, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2016.10.017

Large time control and turnpike properties for wave equations

Author(s): Enrique Zuazua
Published in: Annual Reviews in Control, 44, 2017, Page(s) 199-210, ISSN 1367-5788
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.arcontrol.2017.04.002

Lipschitz dependence of the coefficients on the resolvent and greedy approximation for scalar elliptic problems

Author(s): Mourad Choulli, Enrique Zuazua
Published in: Comptes Rendus Mathematique, 354/12, 2016, Page(s) 1174-1187, ISSN 1631-073X
Publisher: Elsevier Masson
DOI: 10.1016/j.crma.2016.10.017

Null-controllability properties of the wave equation with a second order memory term

Author(s): Umberto Biccari, Sorin Micu
Published in: Journal of Differential Equations, 267/2, 2019, Page(s) 1376-1422, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2019.02.009

Dynamics and control for multi-agent networked systems: A finite-difference approach

Author(s): Umberto Biccari, Dongnam Ko, Enrique Zuazua
Published in: Mathematical Models and Methods in Applied Sciences, 29/04, 2019, Page(s) 755-790, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202519400050

Phase portrait control for 1D monostable and bistable reaction–diffusion equations

Author(s): Camille Pouchol, Emmanuel Trélat, Enrique Zuazua
Published in: Nonlinearity, 32/3, 2019, Page(s) 884-909, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/aaf07e

Internal Observability for Coupled Systems of Linear Partial Differential Equations

Author(s): Pierre Lissy, Enrique Zuazua
Published in: SIAM Journal on Control and Optimization, 57/2, 2019, Page(s) 832-853, ISSN 0363-0129
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/17m1119160

A Two-Dimensional “Flea on the Elephant” Phenomenon and its Numerical Visualization

Author(s): Roberta Bianchini, Laurent Gosse, Enrique Zuazua
Published in: Multiscale Modeling & Simulation, 17/1, 2019, Page(s) 137-166, ISSN 1540-3459
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m1179985

Greedy optimal control for elliptic problems and its application to turnpike problems

Author(s): Víctor Hernández-Santamaría, Martin Lazar, Enrique Zuazua
Published in: Numerische Mathematik, 141/2, 2019, Page(s) 455-493, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-018-1005-z

Controllability and positivity constraints in population dynamics with age structuring and diffusion

Author(s): Debayan Maity, Marius Tucsnak, Enrique Zuazua
Published in: Journal de Mathématiques Pures et Appliquées, 2018, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2018.12.006

Minimal controllability time for finite-dimensional control systems under state constraints

Author(s): Jérôme Lohéac, Emmanuel Trélat, Enrique Zuazua
Published in: Automatica, 96, 2018, Page(s) 380-392, ISSN 0005-1098
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.automatica.2018.07.010

Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential

Author(s): Umberto Biccari
Published in: Mathematical Control & Related Fields, 9/1, 2019, Page(s) 191-219, ISSN 2156-8499
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/mcrf.2019011

Allee optimal control of a system in ecology

Author(s): Emmanuel Trélat, Jiamin Zhu, Enrique Zuazua
Published in: Mathematical Models and Methods in Applied Sciences, 28/09, 2018, Page(s) 1665-1697, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s021820251840002x

Controllability under positivity constraints of semilinear heat equations

Author(s): Dario Pighin, Enrique Zuazua
Published in: Mathematical Control & Related Fields, 8/3, 2018, Page(s) 935-964, ISSN 2156-8499
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/mcrf.2018041

Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions

Author(s): Yannick Privat, Emmanuel Trélat, Enrique Zuazua
Published in: Calculus of Variations and Partial Differential Equations, 58/2, 2019, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-019-1522-3

Analysis of random non-autonomous logistic-type differential equations via the Karhunen–Loève expansion and the Random Variable Transformation technique

Author(s): J.-C. Cortés, A. Navarro-Quiles, J.-V. Romero, M.-D. Roselló
Published in: Communications in Nonlinear Science and Numerical Simulation, 72, 2019, Page(s) 121-138, ISSN 1007-5704
Publisher: Elsevier BV
DOI: 10.1016/j.cnsns.2018.12.013

(CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications

Author(s): Juan Carlos Cortés, Ana Navarro-Quiles, José-Vicente Romero, María-Dolores Roselló
Published in: Mathematical Methods in the Applied Sciences, 2019, ISSN 0170-4214
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/mma.5440

A probabilistic analysis of a Beverton-Holt-type discrete model: Theoretical and computing analysis

Author(s): J.-C. Cortés, A. Navarro-Quiles, J.-V. Romero, M.-D. Roselló
Published in: Computational and Mathematical Methods, 1/1, 2019, Page(s) e1013, ISSN 2577-7408
Publisher: Wiley
DOI: 10.1002/cmm4.1013

The Poisson equation from non-local to local

Author(s): Umberto Biccari and Víctor Hernández-Santamaría
Published in: Electronic Journal of Differential Equations, 145, 2018, Page(s) 1-13, ISSN 1072-6691
Publisher: Texas State University - San Marcos

Addendum: Local Elliptic Regularity for the Dirichlet Fractional Laplacian

Author(s): Umberto Biccari, Mahamadi Warma, Enrique Zuazua
Published in: Advanced Nonlinear Studies, 17/4, 2017, ISSN 1536-1365
Publisher: UTHSCSA Press
DOI: 10.1515/ans-2017-6020

From averaged to simultaneous controllability

Author(s): Jérôme Lohéac, Enrique Zuazua
Published in: Annales de la faculté des sciences de Toulouse Mathématiques, 25/4, 2016, Page(s) 785-828, ISSN 0240-2963
Publisher: University of Tolouse
DOI: 10.5802/afst.1511

Optimal shape design for 2D heat equations in large time

Author(s): Emmanuel Trélat, Can Zhang and Enrique Zuazua
Published in: J. Appl. Funct. Anal., 3, 2018, Page(s) 255-269, ISSN 2189-3764
Publisher: Yokohama publishers

Null Controllability of Linear and Semilinear Nonlocal Heat Equations with an Additive Integral Kernel

Author(s): Umberto Biccari, Víctor Hernández-Santamaría
Published in: SIAM Journal on Control and Optimization, 57/4, 2019, Page(s) 2924-2938, ISSN 0363-0129
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m1218431

Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids

Author(s): M. Morales-Hernández, E. Zuazua
Published in: Computational and Applied Mathematics, 38/4, 2019, ISSN 2238-3603
Publisher: Springer
DOI: 10.1007/s40314-019-0935-0

Null controllability for wave equations with memory

Author(s): Qi Lü, Xu Zhang, Enrique Zuazua
Published in: Journal de Mathématiques Pures et Appliquées, 108/4, 2017, Page(s) 500-531, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2017.05.001

OUP accepted manuscript

Author(s): Umberto Biccari and Víctor Hernández-Santamaría
Published in: Ima Journal Of Mathematical Control And Information, 2018, ISSN 0265-0754
Publisher: Oxford University Press
DOI: 10.1093/imamci/dny025

Controllability of shadow reaction-diffusion systems

Author(s): Víctor Hernández-Santamaría, Enrique Zuazua
Published in: Journal of Differential Equations, 2019, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2019.10.012

Internal Controllability for Parabolic Systems Involving Analytic Non-local Terms

Author(s): Pierre Lissy, Enrique Zuazua
Published in: Chinese Annals of Mathematics, Series B, 39/2, 2018, Page(s) 281-296, ISSN 0252-9599
Publisher: World Scientific Publishing Co
DOI: 10.1007/s11401-018-1064-6

Decay rates for $1-d$ heat-wave planar networks

Author(s): Zhong-Jie Han, Enrique Zuazua
Published in: Networks and Heterogeneous Media, 11/4, 2016, Page(s) 655-692, ISSN 1556-1801
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/nhm.2016013

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

Author(s): Hyeong-Ohk Bae, Seung-Yeal Ha, Jeongho Kim, Dongnam Ko, Sung-Ik Sohn
Published in: SIAM Journal on Mathematical Analysis, 51/3, 2019, Page(s) 2390-2424, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m122025x

Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects

Author(s): Umberto Biccari, Víctor Hernández-Santamaría
Published in: IMA Journal of Mathematical Control and Information, 36/4, 2018, Page(s) 1199-1235, ISSN 0265-0754
Publisher: Oxford University Press
DOI: 10.1093/imamci/dny025

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

Author(s): Umberto Biccari, Mahamadi Warma, Enrique Zuazua
Published in: Communications on Pure & Applied Analysis, 19/4, 2020, Page(s) 1949-1978, ISSN 1553-5258
Publisher: AIMS
DOI: 10.3934/cpaa.2020086

A Stochastic Approach to the Synchronization of Coupled Oscillators

Author(s): Umberto Biccari, Enrique Zuazua
Published in: Frontiers in Energy Research, 8, 2020, ISSN 2296-598X
Publisher: Frontiers
DOI: 10.3389/fenrg.2020.00115

Nonnegative control of finite-dimensional linear systems

Author(s): Jérôme Lohéac, Emmanuel Trélat, Enrique Zuazua
Published in: Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2020, ISSN 0294-1449
Publisher: Elsevier BV
DOI: 10.1016/j.anihpc.2020.07.004

Output controllability in a long-time horizon

Author(s): Martin Lazar, Jérôme Lohéac
Published in: Automatica, 113, 2020, Page(s) 108762, ISSN 0005-1098
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.automatica.2019.108762

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

Author(s): Umberto Biccari, Mahamadi Warma
Published in: Evolution Equations & Control Theory, 9/2, 2020, Page(s) 399-430, ISSN 2163-2480
Publisher: AIMS
DOI: 10.3934/eect.2020011

Shape turnpike for linear parabolic PDE models

Author(s): Gontran Lance, Emmanuel Trélat, Enrique Zuazua
Published in: Systems & Control Letters, 142, 2020, Page(s) 104733, ISSN 0167-6911
Publisher: Elsevier BV
DOI: 10.1016/j.sysconle.2020.104733

Turnpike in optimal shape design

Author(s): G. Lance, E. Trélat, E. Zuazua
Published in: IFAC-PapersOnLine, 52/16, 2019, Page(s) 496-501, ISSN 2405-8963
Publisher: Elsevier
DOI: 10.1016/j.ifacol.2019.12.010

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

Author(s): Dongnam Ko, Enrique Zuazua
Published in: Mathematical Models and Methods in Applied Sciences, 30/04, 2020, Page(s) 765-804, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202520400047

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

Author(s): Seung-Yeal Ha, Dongnam Ko, Woojoo Shim, Hui Yu
Published in: Mathematical Models and Methods in Applied Sciences, 30/04, 2020, Page(s) 727-763, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202520400035

Emergent collective behaviors of stochastic kuramoto oscillators

Author(s): Seung-Yeal Ha, Dongnam Ko, Chanho Min, Xiongtao Zhang
Published in: Discrete & Continuous Dynamical Systems - B, 25/3, 2020, Page(s) 1059-1081, ISSN 1553-524X
Publisher: AIMS
DOI: 10.3934/dcdsb.2019208

Null-controllability of perturbed porous medium gas flow

Author(s): Borjan Geshkovski
Published in: ESAIM: Control, Optimisation and Calculus of Variations, 2020, ISSN 1292-8119
Publisher: EDP Sciences
DOI: 10.1051/cocv/2020009

Propagation of One- and Two-Dimensional Discrete Waves Under Finite Difference Approximation

Author(s): Umberto Biccari, Aurora Marica, Enrique Zuazua
Published in: Foundations of Computational Mathematics, 2020, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-020-09445-0

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

Author(s): Jan Heiland, Enrique Zuazua
Published in: SIAM Journal on Control and Optimization, 03630129, 2021, Page(s) 3600-3624, ISSN 0363-0129
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1356105

Rotor imbalance suppression by optimal control

Author(s): Matteo Gnuffi; Dario Pighin; Noboru Sakamoto
Published in: Optimal Control Applications and Methods, 10991514, 2022, Page(s) 213-242, ISSN 1099-1514
Publisher: John Wiley & Sons Ltd
DOI: 10.1002/oca.2780

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

Author(s): J.-C. Cortés, A. Navarro-Quiles, J.-V. Romero, M.-D. Roselló, Enrique Zuazua
Published in: Journal of the Franklin Institute, 357/12, 2020, Page(s) 8156-8180, ISSN 0016-0032
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.jfranklin.2020.06.005

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

Author(s): Azahar Monge, Enrique Zuazua
Published in: Systems & Control Letters, 145, 2020, Page(s) 104801, ISSN 0167-6911
Publisher: Elsevier BV
DOI: 10.1016/j.sysconle.2020.104801

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

Author(s): Carlos Esteve, Hicham Kouhkouh, Dario Pighin, Enrique Zuazua.
Published in: Mathematics of Control Signals and Systems, 09324194, 2022, ISSN 0932-4194
Publisher: Springer Verlag
DOI: 10.1007/s00498-022-00325-2

Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects

Null Controllability of a nonlinear age, space and two-sex structured population dynamics model

Author(s): Yacouba Simporé; Oumar Traore
Published in: Mathematical Control and Related Fields, 21568472, 2021, ISSN 2156-8472
Publisher: American Institute of Mathematical Sciences
DOI: 10.48550/arxiv.2009.04351

Nonuniqueness of minimizers for semilinear optimal control problems

Author(s): Dario Pighin
Published in: Journal of the European Mathematical Society, 14359855, 2022, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1232

Flow decomposition for heat equations with memory

Author(s): Wang, Gengsheng; Zhang, Yubiao; Zuazua, Enrique
Published in: Journal de Mathématiques Pures et Appliquées, 00217824, 2022, Page(s) 183-215, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.48550/arxiv.2101.09867

A Fragmentation Phenomenon for a Nonenergetic Optimal Control Problem: Optimization of the Total Population Size in Logistic Diffusive Models

Author(s): Idriss Mazari, Domènec Ruiz-Balet
Published in: SIAM Journal on Applied Mathematics, 81/1, 2021, Page(s) 153-172, ISSN 0036-1399
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m132818x

Controllability of shadow reaction-diffusion systems

Author(s): Víctor Hernández-Santamaría, Enrique Zuazua
Published in: Journal of Differential Equations, 268/7, 2020, Page(s) 3781-3818, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2019.10.012

Controllability of One-Dimensional Viscous Free Boundary Flows

Author(s): Borjan Geshkovski, Enrique Zuazua
Published in: SIAM Journal on Control and Optimization, 59/3, 2021, Page(s) 1830-1850, ISSN 0363-0129
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1285354

Control and Numerical approximation of Fractional Diffusion Equations

Author(s): Umberto Biccari, Mahamadi Warma, Enrique Zuazua
Published in: Handbok of Numerical Analysis, 2022, ISBN 9780323853392
Publisher: Elsevier
DOI: 10.1016/bs.hna.2021.12.001

Controllability Under Positivity Constraints of Multi-d Wave Equations

Author(s): Dario Pighin, Enrique Zuazua
Published in: Trends in Control Theory and Partial Differential Equations, 32, 2019, Page(s) 195-232, ISBN 978-3-030-17948-9
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-17949-6_11

The finite-time turnpike phenomenon for optimal control problems: stabilization by non-smooth tracking terms

Author(s): M. Gugat, M. Schuster and E. Zuazua.
Published in: Stabilization of Distributed Parameter Systems: Design Methods and Applications, ICIAM 2019 SEMA SIMAI Springer Series, 2, 2021, Page(s) 17-42, ISSN 2199-3041
Publisher: Springer

Local Regularity for Fractional Heat Equations

Author(s): Umberto Biccari, Mahamadi Warma, Enrique Zuazua
Published in: Recent Advances in PDEs: Analysis, Numerics and Control - In Honor of Prof. Fernández-Cara's 60th Birthday, 17, 2018, Page(s) 233-249, ISBN 978-3-319-97612-9
Publisher: Springer International Publishing
DOI: 10.1007/978-3-319-97613-6_12

Filtered Gradient Algorithms for Inverse Design Problems of One-Dimensional Burgers Equation

Author(s): Laurent Gosse, Enrique Zuazua
Published in: Innovative Algorithms and Analysis, 16, 2017, Page(s) 197-227, ISBN 978-3-319-49261-2
Publisher: Springer International Publishing
DOI: 10.1007/978-3-319-49262-9_7

A Parabolic Approach to the Control of Opinion Spreading

Author(s): Domènec Ruiz-Balet, Enrique Zuazua
Published in: Applied Wave Mathematics II - Selected Topics in Solids, Fluids, and Mathematical Methods and Complexity, 6, 2019, Page(s) 343-363, ISBN 978-3-030-29950-7
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-29951-4_15

Controllability Under Positivity Constraints of Multi-d Wave Equations

Multilevel selective harmonic modulation by duality

Author(s): Umberto Biccari, Enrique Zuazua
Published in: IFAC-PapersOnLine, 24058963, 2022, Page(s) 56-61, ISSN 2405-8963
Publisher: Elsevier
DOI: 10.1016/j.ifacol.2022.08.081

Optimal driving strategies for traffic control with autonomous vehicles

Author(s): Thibault Liard; Raphael Stern; Maria Laura Delle Monache
Published in: IFAC-PapersOnLine, 2020, Page(s) 5332-5329
Publisher: Elsevier
DOI: 10.1016/j.ifacol.2020.12.1219

The turnpike property in nonlinear optimal control — A geometric approach

Author(s): Noboru Sakamoto, Dario Pighin, Enrique Zuazua
Published in: 2019 IEEE 58th Conference on Decision and Control (CDC), 2019, Page(s) 2422-2427, ISBN 978-1-7281-1398-2
Publisher: IEEE
DOI: 10.1109/cdc40024.2019.9028863

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