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Article Dans Une Revue Journal of Differential Equations Année : 2020

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

Yacine Chitour
Swann Marx

Résumé

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation with Dirichlet boundary conditions subject to a nonlinear distributed damping with an L p functional framework, p ∈ [2, ∞]. 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 are proved by considering an appropriate functional of the energy in the desired functional spaces introduced by Haraux in [A. Haraux, Int. J. Math. Modelling Num. Opt., 2009]. Asymptotic behavior analysis is based on an attractivity result on a trajectory of an infinite-dimensional linear time-varying system with a special structure, which relies on the introduction of a suitable Lyapunov functional. Note that some of the results of this paper apply for a large class of nonmonotone dampings.
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Dates et versions

hal-02193922 , version 1 (25-07-2019)
hal-02193922 , version 2 (02-10-2020)

Identifiants

Citer

Yacine Chitour, Swann Marx, Christophe Prieur. $L^p$-asymptotic stability analysis of a 1D wave equation with a nonlinear damping. Journal of Differential Equations, 2020, 269 (10), pp.8107-8131. ⟨10.1016/j.jde.2020.06.007⟩. ⟨hal-02193922v2⟩
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