Volume 28, 2022
|Number of page(s)||32|
|Published online||11 January 2022|
Lp-asymptotic stability of 1D damped wave equations with localized and linear damping★
UMA, ENSTA Paris, Institut Polytechnique de Paris,
2 Département de Mathématiques, Université Abou Bekr Belkaid, Tlemcen, Algeria.
3 L2S, Université Paris Saclay, France.
** Corresponding author: firstname.lastname@example.org
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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