Uniform stabilization of an electromagnetic-elasticity problem in exterior domains

Marcio V. Ferreira; Gustavo Alberto Perla Menzala

doi:10.3934/dcds.2007.18.719

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2007, Volume 18, Issue 4: 719-746. Doi: 10.3934/dcds.2007.18.719

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Uniform stabilization of an electromagnetic-elasticity problem in exterior domains

Marcio V. Ferreira^1, and
Gustavo Alberto Perla Menzala^2,

1.
Franciscan University Center, Rua dos Andradas, 1614, Santa Maria, 97010-032, RS
2.
National Laboratory of Scientific Computation, LNCC/MCT, Av. Getulio Vargas 333, Quitandinha, Petrópolis, RJ, 25651-070

Received: July 2006

Revised: December 2006

Published: October 2007

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Abstract

A coupled system of dynamic hyperbolic equations in electroma- gnetic-elasticity theory in the exterior of an open bounded obstacle $\mathcal{O}$ in 3-D is considered. In the presence of dissipative effects we obtain uniform decay rates of the solution as $t \rightarrow +\infty$. We do not require geometric assumptions on the obstacle or extra assumptions on the initial data. We apply our results to study the above system with a nonlinear perturbation, showing that the solutions hold the same rate of decay provided the initial data is "small" in a suitable sense. Previous results of this type have recently been obtained for the scalar wave equation by M. Nakao [18, 19] and R. Ikehata [8].

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Mathematics Subject Classification: Primary: 35Q99, 35Q60; Secondary: 35L99.

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