# $L^p$-asymptotic stability analysis of a 1D wave equation with a boundary nonmonotone damping

3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France
Abstract : This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation with a nonlinear non-monotone damping acting at a boundary. The study is performed in an $L^p$-functional framework, $p\in [1,\infty]$. Some well-posedness results are provided together with exponential decay to zero of trajectories, with an estimation of the decay rate. The well-posedness results rely mainly on some results collected in [7]. Asymptotic behavior results are obtained by the use of a suitable Lyapunov functional if $p$ is finite and on a trajectory-based analysis if $p=\infty$.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :
Complete list of metadatas

Cited literature [8 references]

https://hal.archives-ouvertes.fr/hal-02463413
Contributor : Guilherme Mazanti <>
Submitted on : Friday, January 31, 2020 - 9:32:49 PM
Last modification on : Monday, February 17, 2020 - 11:26:28 AM

### File

nonlinear-boundary-wave.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-02463413, version 1

### Citation

Swann Marx, Guilherme Mazanti. $L^p$-asymptotic stability analysis of a 1D wave equation with a boundary nonmonotone damping. 2020. ⟨hal-02463413⟩

Record views

Files downloads