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Measure attractors and random attractors for stochastic partial differential equations

 

作者: B. Schmalfuβ,  

 

期刊: Stochastic Analysis and Applications  (Taylor Available online 1999)
卷期: Volume 17, issue 6  

页码: 1075-1101

 

ISSN:0736-2994

 

年代: 1999

 

DOI:10.1080/07362999908809649

 

出版商: Marcel Dekker, Inc.

 

数据来源: Taylor

 

摘要:

In the theory of stochastic differential equations we can distinguish between two kinds of attractors. The first one is the attractor (measure attractor) with respect to the Markov semigroup generated by a stochastic differential equation. The second meaning of attractors (random attractors) is to be understood with respect to each trajectory of the random equation. The aim of this paper is to bring together the two meanings of attractors. In particular, we show the existence of measure attractors if random attractors exist. We can also show the uniqueness of the stationary distributions of the stochastic Navier-Stokes equation if the viscosity is large

 

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