A Dynamical Approximation for Stochastic Partial Differential Equations
نویسنده
چکیده
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the random invariant manifold is almost surely asymptotically complete. The asymptotic dynamical behavior is thus described by a stochastic ordinary differential system on the random invariant manifold, under suitable conditions. As an application, stationary states (invariant measures) is considered for one example of stochastic partial differential equations. Date: July 16, 2007(revised version); May 4, 2007(original version). 2000 Mathematics Subject Classification. Primary 37L55, 35R60; Secondary 60H15, 37H20, 34D35.
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