Invariant manifolds for stochastic partial differential equations
Duan, Jinqiao ; Lu, Kening ; Schmalfuss, Björn
Ann. Probab., Tome 31 (2003) no. 1, p. 2109-2135 / Harvested from Project Euclid
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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.
Publié le : 2003-10-14
Classification:  Invariant manifolds,  cocycles,  nonautonomous dynamical systems,  stochastic partial differential equations,  generalized fixed points,  60H15,  37H10,  37L55,  37L25,  37D10 
@article{1068646380,
     author = {Duan, Jinqiao and Lu, Kening and Schmalfuss, Bj\"orn},
     title = {Invariant manifolds for stochastic partial differential equations},
     journal = {Ann. Probab.},
     volume = {31},
     number = {1},
     year = {2003},
     pages = { 2109-2135},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1068646380}
}

Duan, Jinqiao; Lu, Kening; Schmalfuss, Björn. Invariant manifolds for stochastic partial differential equations. Ann. Probab., Tome 31 (2003) no. 1, pp.  2109-2135. http://gdmltest.u-ga.fr/item/1068646380/