ABSTRACT
Wave motion and mechanical vibration are two of the most commonly observed physical phenomena. As mathematical models, they are usually described by partial differential equations of hyperbolic type. The most well-known one is the wave equation. This chapter briefly reviews some basic definitions of hyperbolic equations and studies the existence of solutions to some linear and semilinear stochastic wave equations in a bounded domain. As in the parabolic case, it employs the Green’s function approach based on the method of eigenfunctions expansion. The Green's function approach coupled with the method of Fourier transform is used to analyze stochastic wave equations in an unbounded domain. The chapter also studies the solutions of a class of linear and semilinear stochastic hyperbolic systems.
