Invariant measures for stochastic nonlinear beam and wave equations

0453412 - ÚTIA 2016 RIV US eng J - Journal Article
Brzezniak, Z. - Ondreját, Martin - Seidler, Jan
Invariant measures for stochastic nonlinear beam and wave equations.
Journal of Differential Equations. Roč. 260, č. 5 (2016), s. 4157-4179. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA ČR GAP201/10/0752
Institutional support: RVO:67985556
Keywords : stochastic partial differential equation * stochastic beam equation * stochastic wave equation * invariant measure
Subject RIV: BA - General Mathematics
Impact factor: 1.988, year: 2016
http://library.utia.cas.cz/separaty/2016/SI/ondrejat-0453412.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0257064