Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (1): 158-172.

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Random Attractors for the Stochastic Nonclassical Diffusion Equation on Unbounded Domains

Li Dingshi, Fan Yingfei   

  1. School of Mathematics, Southwest Jiaotong University, Chengdu 610031
  • Received:2016-04-19 Revised:2016-09-07 Online:2017-02-26 Published:2017-02-26
  • Supported by:

    Supported by the NSFC (11271270, 11326118, 11501065, 11201320) and the Fundamental Research Funds for the Central Universities (2682015CX059)

Abstract:

In this paper, we prove the existence and uniqueness of a random attractor for a stochastic nonclassical diffusion equation on unbounded domains with additive noise. To overcome the difficulty caused by the non-compactness of Sobolev embeddings on unbounded domains, a cut-off method and a decomposition trick are combined to prove the asymptotic compactness of the solutions.

Key words: Stochastic nonclassical diffusion equation, Random attractor, Asymptotic compactness

CLC Number: 

  • O175.26
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