Invariant manifolds for stochastic partial differential equations

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dc.creatorDuan, Jinqiao
dc.creatorLu, Kening
dc.creatorSchmalfuss, Bjoern
dc.date2004-09-24
dc.date.accessioned2026-07-07T06:32:57Z
dc.date.available2026-07-07T06:32:57Z
dc.descriptionInvariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant manifolds for infinite dimensional {\em random} dynamical systems generated by {\em stochastic} partial differential equations. We first introduce a random graph transform and a fixed point theorem for non-autonomous systems. Then we show the existence of generalized fixed points which give the desired invariant manifolds.
dc.identifierhttps://arxiv.org/abs/math/0409485
dc.identifierhttp://arxiv.org/abs/math/0409485
dc.identifierAnnals of Probability 31(2003), 2109-2135
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99035
dc.subjectDynamical Systems
dc.subjectAnalysis of PDEs
dc.subject60H15; 37H10;37L55;37L25; 37D10
dc.titleInvariant manifolds for stochastic partial differential equations
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