On a stochastic hyperbolic system in linear elasticity

Abstract

In this paper we discuss the Cauchy problem for linear elasticity with a space-time white noise forcing term. We show that the solution can be represented by a formula analogous to the Riesz formula for solutions of a wave equation. The solution is a generalized stochastic process and is obtained as the limit of a sequence of ordinary stochastic processes. Our basic tool is the Hilbert space method combined with geometric properties of solutions inherent with a hyperbolic system.