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Invariant manifolds for stochastic partial differential equations

Invariant manifolds for stochastic partial differential equations.

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Oct 2003Embargo end date: 01 Jan 2004Publisher:Institute of Mathematical StatisticsJournal:The Annals of Probability, volume 31 (issn: 0091-1798,

Authors: Duan, Jinqiao; Lu, Kening; Schmalfuss, Björn;

doi: 10.1214/aop/1068646380 , 10.48550/arxiv.math/0409485

arXiv: http://arxiv.org/abs/math/0409485

Invariant manifolds for stochastic partial differential equations

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Abstract

Invariant 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.

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University of Science and Technology of China
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Michigan State University
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Keywords

invariant manifolds, 37D10, stochastic partial differential equations, 37L55, generalized fixed point, Dynamical Systems (math.DS), 37H10, Mathematics - Analysis of PDEs, Stochastic partial differential equations (aspects of stochastic analysis), 37L25, FOS: Mathematics, Mathematics - Dynamical Systems, generalized fixed points, cocycles, nonautonomous dynamical systems, Invariant manifold theory for dynamical systems, stochastic partial differential equation, Invariant manifolds, Infinite-dimensional random dynamical systems; stochastic equations, 60H15, 60H15; 37H10;37L55;37L25; 37D10, Generation, random and stochastic difference and differential equations, Analysis of PDEs (math.AP)

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	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%