%0 Journal Article %T Lp-asymptotic stability of 1D damped wave equations with localized and linear damping %+ Optimisation et commande (OC) %+ Département de Mathematiques [Tlemcen] %A Kafnemer, Meryem %A Benmiloud, Mebkhout %A Jean, Frédéric %A Chitour, Yacine %Z iCODE Institute, research project of the IDEX Paris-Saclay %Z 32 pages %< avec comité de lecture %@ 1292-8119 %J ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %8 2022-01-11 %D 2022 %Z 2104.05679 %R 10.1051/cocv/2021107 %Z Mathematics [math]/Analysis of PDEs [math.AP] %Z Mathematics [math]/Optimization and Control [math.OC]Journal articles %X In this paper, we study the $L^p$-asymptotic stability of the one-dimensional linear damped wave equation with Dirichlet boundary conditions in $[0,1]$, with $p\in (1,\infty)$. The damping term is assumed to be linear and localized to an arbitrary open sub-interval of $[0,1]$. We prove that the semi-group $(S_p(t))_{t\geq 0}$ associated with the previous equation is well-posed and exponentially stable. The proof relies on the multiplier method and depends on whether $p\geq 2$ or $1