Invariant measures for stochastic nonlinear beam and wave equations

Zdzislaw Brzezniak; Martin Ondreját; J. Seidler

doi:10.1016/j.jde.2015.11.007

Invariant measures for stochastic nonlinear beam and wave equations

Zdzislaw Brzezniak, Martin Ondreját, J. Seidler

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	4157–4179
Number of pages	23
Journal	Journal of Differential Equations
Volume	260
Issue number	5
Early online date	28 Nov 2015
DOIs	https://doi.org/10.1016/j.jde.2015.11.007
Publication status	Published - 5 Mar 2016

Bibliographical note

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10.1016/j.jde.2015.11.007

Brz+Ondr+S_2015_YJDEQ8136_new
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Cite this

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AU - Ondreját, Martin

AU - Seidler, J.

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N2 - 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.

AB - 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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DO - 10.1016/j.jde.2015.11.007

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