English

Stabilization of two strongly coupled hyperbolic equations in exterior domains

Analysis of PDEs 2019-05-22 v1

Abstract

In this paper we study the behavior of the total energy and the L2L^2-norm of solutions of two coupled hyperbolic equations by velocities in exterior domains. Only one of the two equations is directly damped by a localized damping term. We show that, when the damping set contains the coupling one and the coupling term is effective at infinity and on captive region, then the total energy decays uniformly and the L2L^2-norm of smooth solutions is bounded. In the case of two Klein-Gordon equations with equal speeds we deduce an exponential decay of the energy.

Keywords

Cite

@article{arxiv.1905.08370,
  title  = {Stabilization of two strongly coupled hyperbolic equations in exterior domains},
  author = {L. Aloui and H. Azaza},
  journal= {arXiv preprint arXiv:1905.08370},
  year   = {2019}
}