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November  2007, 18(4): 719-746. doi: 10.3934/dcds.2007.18.719

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, Brazil
2. 

National Laboratory of Scientific Computation, LNCC/MCT, Av. Getulio Vargas 333, Quitandinha, Petrópolis, RJ, 25651-070, Brazil

Received  July 2006 Revised  December 2006 Published  May 2007

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].
Keywords: exterior domain, electromagnetic-elasticity, uniform stabilization, semilinear problem..
Mathematics Subject Classification: Primary: 35Q99, 35Q60; Secondary: 35L9.
Citation: Marcio V. Ferreira, Gustavo Alberto Perla Menzala. Uniform stabilization of an electromagnetic-elasticity problem in exterior domains. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 719-746. doi: 10.3934/dcds.2007.18.719
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