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Stochastic wave equations with dissipative damping. (English) Zbl 1122.60056
For a stochastic wave equation with nonlinear damping in a bounded open set in n perturbed additively by a trace class Wiener process, growth conditions on the nonlinearity are given to ensure existence of an invariant measure for the associated Markov semigroup. A strengthened version of these conditions is shown to imply uniqueness of the invariant measure. The methods essentially rest upon employing suitable Lyapunov functions in order to obtain tightness and exponential decay properties, respectively.
MSC:
60H15Stochastic partial differential equations
37L40Invariant measures (infinite-dimensional dissipative systems)