Decaying and nondecaying properties of the local energy of an elastic wave outside an obstacle

Abstract

We consider the decaying mode of the local energy of the solution of an initial boundary value problem in the exterior region outside a spherical obstacle for the equation of elasticity as time tends to infinity. It is shown that Rayleigh’s surface wave prevents the exponential decay of the local energy in the case of the Neumann boundary condition and that the local energy blows up at the rate of the square of the time variable in the case of the Robin boundary condition.