#### 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

#### Recommended Citation

Chow, Pao-Liu, "Asymptotic Solutions of Semilinear Stochastic Wave Equations" (2004). *Mathematics Research Reports*. 25.

https://digitalcommons.wayne.edu/math_reports/25

## Comments

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