Lp-asymptotic stability of 1D damped wave equations with localized and linear damping - ENSTA Paris - École nationale supérieure de techniques avancées Paris Access content directly
Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2022

Lp-asymptotic stability of 1D damped wave equations with localized and linear damping

Meryem Kafnemer
Frédéric Jean
Yacine Chitour

Abstract

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
Fichier principal
Vignette du fichier
cocv210066.pdf (817.33 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-03196874 , version 1 (05-03-2024)

Identifiers

Cite

Meryem Kafnemer, Mebkhout Benmiloud, Frédéric Jean, Yacine Chitour. Lp-asymptotic stability of 1D damped wave equations with localized and linear damping. ESAIM: Control, Optimisation and Calculus of Variations, 2022, ⟨10.1051/cocv/2021107⟩. ⟨hal-03196874⟩
121 View
2 Download

Altmetric

Share

Gmail Facebook X LinkedIn More