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

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
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Preprints, Working Papers, ...
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https://hal-ensta-paris.archives-ouvertes.fr//hal-03196874
Contributor : Frédéric Jean Connect in order to contact the contributor
Submitted on : Tuesday, April 13, 2021 - 12:02:13 PM
Last modification on : Wednesday, April 14, 2021 - 3:33:53 AM

### Identifiers

• HAL Id : hal-03196874, version 1
• ARXIV : 2104.05679

### Citation

Meryem Kafnemer, Mebkhout Benmiloud, Frédéric Jean, Yacine Chitour. Lp-asymptotic stability of 1D damped wave equations with localized and linear damping. 2021. ⟨hal-03196874⟩

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