Invariant measures for stochastic nonlinear beam and wave equations

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Brzezniak, Zdzislaw ; Ondreját, Martin ; Seidler, J. (2016)

Existence of an invariant measure for a stochastic extensible beam equation and for a stochastic damped wave equation with polynomial nonlinearities is proved. It is shown first that the corresponding transition semigroups map the space of all bounded sequentially weakly continuous functions on the state space into itself and then by a Lyapunov functions approach solutions bounded in probability are found.
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    • we recall that BT (C([0, T ]; Xw)) is the σ-algebra on C([0, T ]; Xw) generated by the mappings C([0, T ]; Xw) → X : h 7→ h(s) for s ∈ [0, T ]. Zdzislaw Brze´zniak, Department of Mathematics, University of York, York, YO10 5DD, zb500@york.ac.uk, tel: +44 1904 32 4154, fax: +44 1904 32 3071 Martin Ondreja´t, Institute of Information Theory and Automation of the ASCR, Pod Voda´renskou veˇˇz´ı 4, CZ-182 08, Praha 8, Czech Republic, ondrejat@utia.cas.cz, phone: ++ 420 266 052 284, fax: ++ 420 286 890 378 Jan Seidler, Institute of Information Theory and Automation of the ASCR, Pod Voda´renskou veˇˇz´ı 4, CZ-182 08, Praha 8, Czech Republic, seidler@utia.cas.cz, phone: ++ 420 266 052 041, fax: ++ 420 286 890 378

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