Asymptotic stability of wave equations with memory and frictional boundary dampings

Volume 35 / 2008

Fatiha Alabau-Boussouira Applicationes Mathematicae 35 (2008), 247-258 MSC: 35B35, 35B37, 45K05, 93D15, 93D20. DOI: 10.4064/am35-3-1

Abstract

This work is concerned with stabilization of a wave equation by a linear boundary term combining frictional and memory damping on part of the boundary. We prove that the energy decays to zero exponentially if the kernel decays exponentially at infinity. We consider a slightly different boundary condition than the one used by M. Aassila et al. [Calc. Var. 15, 2002]. This allows us to avoid the assumption that the part of the boundary where the feedback is active is strictly star-shaped. The result is based on multiplier techniques and integral inequalities.

Authors

  • Fatiha Alabau-BoussouiraDépartement de Mathématiques
    Université de Metz
    INRIA Projet CORIDA
    Ile du Saulcy
    57045 Metz Cedex 01, France
    e-mail

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