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Zbl 1122.60056
Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano
Stochastic wave equations with dissipative damping. (English)
[J] Stochastic Processes Appl. 117, No. 8, 1001-1013 (2007). ISSN 0304-4149

For a stochastic wave equation with nonlinear damping in a bounded open set in $\Bbb R^n$ 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.
[Hans Crauel (Frankfurt)]

MSC 2000:: *60H15 Stochastic partial differential equations
37L40 Invariant measures

Keywords: stochastic wave equation; Markov semigroup; invariant measure; Lyapunov function

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