Electron. J. Diff. Eqns., Vol. 2006(2006), No. 65, pp. 1-13.

Energy decay for solutions to semilinear systems of elastic waves in exterior domains

Marcio V. Ferreira, Gustavo P. Menzala

Abstract:
We consider the dynamical system of elasticity in the exterior of a bounded open domain in 3-D with smooth boundary. We prove that under the effect of "weak" dissipation, the total energy decays at a uniform rate as $t \to +\infty$, provided the initial data is "small" at infinity. No assumptions on the geometry of the obstacle are required. The results are then applied to a semilinear problem proving global existence and decay for small initial data.

Submitted March 20, 2006. Published May 22, 2006.
Math Subject Classifications: 35Q99, 35L99.
Key Words: Uniform stabilization; exterior domain; system of elastic waves; semilinear problem.

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Marcio V. Ferreira
Centro Universitá:rio Franciscano, Rua dos Andradas 1614
Santa Maria, CEP 97010-032, RS, Brazil
email: ferreira@unifra.br
Gustavo Perla Menzala
National Laboratory of Scientific Computation LNCC/MCT
Av. Getulio Vargas 333, Petropolis, CEP 25651-070, RJ, Brasil
and IM-UFRJ, P.O. Box 68530, RJ, Brazil
email: perla@lncc.br

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