| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 1 | |
| Number of page(s) | 32 | |
| DOI | https://doi.org/10.1051/cocv/2021107 | |
| Published online | 11 January 2022 | |
Lp-asymptotic stability of 1D damped wave equations with localized and linear damping★
1
UMA, ENSTA Paris, Institut Polytechnique de Paris,
91120
Palaiseau, France.
2
Département de Mathématiques, Université Abou Bekr Belkaid,
Tlemcen, Algeria.
3
L2S, Université Paris Saclay, France.
** Corresponding author: kafnemer.meryem@gmail.com
Received:
14
April
2021
Accepted:
1
December
2021
In this paper, we study the Lp-asymptotic stability of the one dimensional linear damped wave equation with Dirichlet boundary conditions in [0, 1], with p ∈ (1, ∞). 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 (Sp(t))t≥0 associated with the previous equation is well-posed and exponentially stable. The proof relies on the multiplier method and depends on whether p ≥ 2 or 1 < p < 2.
Mathematics Subject Classification: 93D20 / 35L05
Key words: Linear / 1D wave / localized / damping / Lp asymptotic stability
© The authors. Published by EDP Sciences, SMAI 2022
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