Uniform stabilization of an electromagnetic-elasticity problem in exterior domains

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 dissipativeeffects we obtain uniform decay rates of the solution as $t\rightarrow +\infty$. We do not require geometric assumptions on theobstacle or extra assumptions on the initial data. We apply ourresults to study the above system with a nonlinear perturbation,showing that the solutions hold the same rate of decay provided theinitial data is 'small' in a suitable sense. Previous results ofthis type have recently been obtained for the scalar wave equationby M. Nakao [18, 19] and R. Ikehata [8].