Energy decay rates of elastic waves in unbounded domain with potential type of damping

In this paper we first show that the total energy of solutions for a semilinear system of elastic waves in R n with a potential type of damping decays in an algebraic rate to zero. We study the critical potential case and we assume that the initial data have a compact support. An application for the Euler–Poisson–Darboux type dissipation V ( t , x ) is obtained and in this case the compactness of the support on the initial data is not necessary. Finally, we shall discuss the energy concentration region for the linear system of elastic waves in an exterior domain.