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Asymptotics of solutions to semilinear stochastic wave equations

Pao-Liu Chow
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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.

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Pao-Liu Chow. 2006-07-04. Asymptotics of solutions to semilinear stochastic wave equations. https://doi.org/10.1214/105051606000000141

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