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October 2003 Invariant manifolds for stochastic partial differential equations
Jinqiao Duan, Kening Lu, Björn Schmalfuss
Ann. Probab. 31(4): 2109-2135 (October 2003). DOI: 10.1214/aop/1068646380


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 random dynamical systems generated by stochastic partial differential equations. We first introduce a random graph transform and a fixed point theorem for nonautonomous systems. Then we show the existence of generalized fixed points which give the desired invariant manifolds.


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Jinqiao Duan. Kening Lu. Björn Schmalfuss. "Invariant manifolds for stochastic partial differential equations." Ann. Probab. 31 (4) 2109 - 2135, October 2003.


Published: October 2003
First available in Project Euclid: 12 November 2003

zbMATH: 1052.60048
MathSciNet: MR2016614
Digital Object Identifier: 10.1214/aop/1068646380

Primary: 60H15
Secondary: 37D10 , 37H10 , 37L25 , 37L55

Keywords: cocycles , generalized fixed points , invariant manifolds , nonautonomous dynamical systems , Stochastic partial differential equations

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 4 • October 2003
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