Asymptotics of solutions to semilinear stochastic wave equations
By Pao-Liu Chow. 2006
46 citations recorded by the source corpus.
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.
View Paper: https://www.semanticscholar.org/paper/d238f380677284a47598f5a2b1762c7065226cff
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Citations in the corpus
- Invariant measures for stochastic nonlinear beam and wave equations (2016, background): “In [7], a damped stochastic wave equation in a bounded domain with nonlinear, but globally Lipschitz continuous nonlinear terms in drift and diffusion is dealt with.”