Asymptotics of solutions to semilinear stochastic wave equations

Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions. the existence theorem fora unique global solution is given. Next the questions of bounded solutions and the exponential stability of an equilibrium solution. in mean-square and the almost sure sense. are studied. Then. under some sufficient conditions. the existence of a unique invariant measure is proved. Two examples are presented to illustrate some applications of the theorems.