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

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 $p=\infty$.
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Submitted on : Friday, January 31, 2020 - 9:32:49 PM
Last modification on : Monday, February 17, 2020 - 11:26:28 AM

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

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