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arXiv · 1907.11712

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

Yacine Chitour·Swann Marx·Christophe Prieur
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Abstract

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 $\in$ [2, $\infty$]. 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 are proved by considering an appropriate functional of the energy in the desired functional spaces introduced by Haraux in [11]. 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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Yacine Chitour, Swann Marx, Christophe Prieur. 2019-07-26. L^p-asymptotic stability analysis of a 1D wave equation with a nonlinear damping. https://arxiv.org/abs/1907.11712

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