Dynamic Control and Numerics of Partial Differential Equations

Publications

Peer reviewed articles (49)

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, Issue 56/2, 2018, Page(s) 1222-1252, ISSN 0363-0129
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, Issue 17/2, 2017, ISSN 1536-1365
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, Issue 55/2, 2017, Page(s) 1128-1152, ISSN 0363-0129
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, Issue 27/09, 2017, Page(s) 1587-1644, ISSN 0218-2025
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, Issue 12/3, 2017, Page(s) 461-488, ISSN 1556-1801
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, Issue 55/4, 2017, Page(s) 2437-2459, ISSN 0363-0129
DOI: 10.1137/151004239

Averaged controllability of parameter dependent conservative semigroups

Author(s): Jérôme Lohéac, Enrique Zuazua
Published in: Journal of Differential Equations, Issue 262/3, 2017, Page(s) 1540-1574, ISSN 0022-0396
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, Issue 44, 2017, Page(s) 199-210, ISSN 1367-5788
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, Issue 354/12, 2016, Page(s) 1174-1187, ISSN 1631-073X
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, Issue 267/2, 2019, Page(s) 1376-1422, ISSN 0022-0396
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, Issue 29/04, 2019, Page(s) 755-790, ISSN 0218-2025
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, Issue 32/3, 2019, Page(s) 884-909, ISSN 0951-7715
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, Issue 57/2, 2019, Page(s) 832-853, ISSN 0363-0129
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, Issue 17/1, 2019, Page(s) 137-166, ISSN 1540-3459
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, Issue 141/2, 2019, Page(s) 455-493, ISSN 0029-599X
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
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, Issue 96, 2018, Page(s) 380-392, ISSN 0005-1098
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, Issue 9/1, 2019, Page(s) 191-219, ISSN 2156-8499
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, Issue 28/09, 2018, Page(s) 1665-1697, ISSN 0218-2025
DOI: 10.1142/s021820251840002x

Controllability under positivity constraints of semilinear heat equations

Author(s): Dario Pighin, Enrique Zuazua
Published in: Mathematical Control & Related Fields, Issue 8/3, 2018, Page(s) 935-964, ISSN 2156-8499
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, Issue 58/2, 2019, ISSN 0944-2669
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, Issue 72, 2019, Page(s) 121-138, ISSN 1007-5704
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
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, Issue 1/1, 2019, Page(s) e1013, ISSN 2577-7408
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, Issue 145, 2018, Page(s) 1-13, ISSN 1072-6691

Addendum: Local Elliptic Regularity for the Dirichlet Fractional Laplacian

Author(s): Umberto Biccari, Mahamadi Warma, Enrique Zuazua
Published in: Advanced Nonlinear Studies, Issue 17/4, 2017, ISSN 1536-1365
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, Issue 25/4, 2016, Page(s) 785-828, ISSN 0240-2963
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., Issue 3, 2018, Page(s) 255-269, ISSN 2189-3764

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, Issue 57/4, 2019, Page(s) 2924-2938, ISSN 0363-0129
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, Issue 38/4, 2019, ISSN 2238-3603
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, Issue 108/4, 2017, Page(s) 500-531, ISSN 0021-7824
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
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
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, Issue 39/2, 2018, Page(s) 281-296, ISSN 0252-9599
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, Issue 11/4, 2016, Page(s) 655-692, ISSN 1556-1801
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, Issue 51/3, 2019, Page(s) 2390-2424, ISSN 0036-1410
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, Issue 36/4, 2018, Page(s) 1199-1235, ISSN 0265-0754
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, Issue 19/4, 2020, Page(s) 1949-1978, ISSN 1553-5258
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, Issue 8, 2020, ISSN 2296-598X
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
DOI: 10.1016/j.anihpc.2020.07.004

Output controllability in a long-time horizon

Author(s): Martin Lazar, Jérôme Lohéac
Published in: Automatica, Issue 113, 2020, Page(s) 108762, ISSN 0005-1098
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, Issue 9/2, 2020, Page(s) 399-430, ISSN 2163-2480
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, Issue 142, 2020, Page(s) 104733, ISSN 0167-6911
DOI: 10.1016/j.sysconle.2020.104733

Turnpike in optimal shape design

Author(s): G. Lance, E. Trélat, E. Zuazua
Published in: IFAC-PapersOnLine, Issue 52/16, 2019, Page(s) 496-501, ISSN 2405-8963
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, Issue 30/04, 2020, Page(s) 765-804, ISSN 0218-2025
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, Issue 30/04, 2020, Page(s) 727-763, ISSN 0218-2025
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, Issue 25/3, 2020, Page(s) 1059-1081, ISSN 1553-524X
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
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
DOI: 10.1007/s10208-020-09445-0

Book chapters (4)

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, Issue 17, 2018, Page(s) 233-249
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, Issue 16, 2017, Page(s) 197-227
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, Issue 6, 2019, Page(s) 343-363
DOI: 10.1007/978-3-030-29951-4_15

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, Issue 32, 2019, Page(s) 195-232
DOI: 10.1007/978-3-030-17949-6_11

Conference proceedings (1)

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
DOI: 10.1109/cdc40024.2019.9028863