Uniform decay rates of coupled anisotropic elastodynamic/Maxwell equations with nonlinear damping

Abstract

This work is devoted to study the asymptotic behavior of the total energy associated with a coupled system of anisotropic hyperbolic models: the elastodynamic equations and Maxwell's system in the exterior of a bounded body in ${\mathbb{R}}^3$. Our main result says that in the presence of nonlinear damping, a unique solution of small initial data exists globally in time and the total energy as well as higher order energies decay at a uniform rate as $t\to +\infty$.