Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 65, pp. 1-13.

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

Authors: Marcio V. Ferreira (Centro Univ. Franciscano, Brazil)
         Gustavo P. Menzala (National Lab. of Scientific Computation. Brazil) 

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.