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Invariant measures for stochastic nonlinear beam and wave equations

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JournalJournal of Differential Equations
DateE-pub ahead of print - 28 Nov 2015
DatePublished (current) - 5 Mar 2016
Issue number5
Volume260
Number of pages23
Pages (from-to)4157–4179
Early online date28/11/15
Original languageEnglish

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.

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© Elsevier 2015. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.

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