Document Type

Technical Report

Abstract

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

2004.07

Disciplines

Applied Mathematics | Mathematics

AMS Subject Classification

Primary 60H15; secondary 60H05

Comments

Supported in part by a grant from the Academy of Applied Science.

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