%0 Journal Article
%T Weak Input to state estimates for 2D damped wave equations with localized and non-linear damping
%+ Unité de Mathématiques Appliquées (UMA)
%+ Optimisation et commande (OC)
%+ Université Aboubekr Belkaid - University of Belkaïd Abou Bekr [Tlemcen]
%+ Laboratoire des signaux et systèmes (L2S)
%A Kafnemer, Meryem
%A Mebkhout, Benmiloud
%A Chitour, Yacine
%< avec comité de lecture
%@ 0363-0129
%J SIAM Journal on Control and Optimization
%I Society for Industrial and Applied Mathematics
%8 2021
%D 2021
%Z 2005.06206
%R 10.1137/20M1337909
%Z Mathematics [math]/Optimization and Control [math.OC]
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X In this paper, we study input-to-state (ISS) issues for damped wave equations with Dirichlet boundary conditions on a bounded domain of dimension two. The damping term is assumed to be non-linear and localized to an open subset of the domain. In a first step, we handle the undisturbed case as an extension of a previous work, where stability results are given with a damping term active on the full domain. Then, we address the case with disturbances and provide input-to-state types of results.
%G English
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-03197202/document
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-03197202/file/Weak%20ISS%20for%20twoD%20damped%20wave%20with%20localized%20nonlinear%20damping.pdf
%L hal-03197202
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-03197202
%~ ENSTA
%~ CNRS
%~ SUP_LSS
%~ INSMI
%~ SUP_SYSTEMES
%~ UMA_ENSTA
%~ CENTRALESUPELEC
%~ TDS-MACS
%~ UNIV-PARIS-SACLAY
%~ IP_PARIS
%~ IP_PARIS_COPIE
%~ TEST-HALCNRS
%~ UNIVERSITE-PARIS-SACLAY
%~ GS-ENGINEERING
%~ GS-COMPUTER-SCIENCE