Asymptotics of solutions to semilinear stochastic wave equations

Details Asymptotics of solutions to semilinear stochastic wave equations Asymptotics of solutions to semilinear stochastic wave equations

2006-07-04

arxiv.org/abs/math/0607097v1

Annals of Applied Probability 2006, Vol. 16, No. 2, 757-789

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000141 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000141

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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