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 for a 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.
Number in Series
Applied Mathematics | Mathematics
AMS Subject Classification
Primary 60H15; secondary 60H05
Chow, Pao-Liu, "Asymptotic Solutions of Semilinear Stochastic Wave Equations" (2004). Mathematics Research Reports. 25.