广西师范大学学报（自然科学版） ›› 2020, Vol. 38 ›› Issue (2): 134-143.doi: 10.16088/j.issn.1001-6600.2020.02.016

• CCIR2019 • 上一篇    下一篇

无界域上非自治随机反应扩散方程一致随机吸引子的存在性

张杰, 李晓军*   

  1. 河海大学理学院,江苏南京210098
  • 收稿日期:2018-12-11 发布日期:2020-04-02
  • 通讯作者: 李晓军(1970—),男,甘肃定西人,河海大学教授,博士。E-mail:lixjun05@hhu.edu.cn
  • 基金资助:
    国家自然科学基金(11571092)

Existence of Uniform Random Attractor for NonautonomousStochastic Reaction-diffusion Equations on Unbounded Domains

ZHANG Jie, LI Xiaojun*   

  1. School of Science, Hehai University, Nanjing Jiangsu 210098, China
  • Received:2018-12-11 Published:2020-04-02

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摘要： 本文研究无界域上一类带有白噪声的非自治随机反应扩散方程一致吸引子的存在性。首先通过对解的一致估计, 证明了对应于原方程的随机动力系统拥有关于符号空间的一致拉回吸收集;其次, 通过渐近尾部估计得到解是一致拉回渐近紧性, 从而得到原系统一致随机吸引子的存在性。

关键词: 随机反应扩散方程, 一致吸引子, 无界域, 白噪声, 渐近紧性

Abstract: This paper studies the existence of uniform attractors for a class of nonautonomous stochastic reaction-diffusion equations with white noise on unbounded domains. Firstly, with uniform estimation of the solutions, it is proved that the stochastic dynamical system corresponding to the original equation has a uniformly with respect to symbol space pullback absorbing set. Secondly, by asymptotic tail estimation, it is proved that the solution is uniformly pullback and asymptotically compact. The existence of uniform random attractor of the original system is obtained.

Key words: tochasticreaction-diffusionequation, uniformattractor, unboundeddomain, whitenoise

中图分类号: 

  • O175.29
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