数学物理学报 ›› 2017, Vol. 37 ›› Issue (1): 158-172.

• 论文 • 上一篇    下一篇

随机非局部扩散方程的随机吸引子的存在性

黎定仕, 范英飞   

  1. 西南交通大学数学学院 成都 610031
  • 收稿日期:2016-04-19 修回日期:2016-09-07 出版日期:2017-02-26 发布日期:2017-02-26
  • 作者简介:黎定仕,E-mail:lidingshi2006@163.com
  • 基金资助:

    国家自然科学基金(11271270,11326118,11501065,11201320)和中央高校基本科研业务费创新基金(2682015CX059)

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)

摘要:

证明了带加性噪声的非局部扩散方程的随机吸引子的存在性和唯一性.为了克服无界区域Sobolev嵌入不紧的问题,该文运用尾估计和分解相结合的方法证明方程解的渐近紧性.

关键词: 随机非局部反应扩散方程, 随机吸引子, 渐近紧

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

中图分类号: 

  • O175.26