数学物理学报 ›› 2016, Vol. 36 ›› Issue (1): 36-48.

• 论文 • 上一篇    下一篇

记忆型非经典反应扩散方程在R3中解的渐近性态

马巧珍, 徐玲, 张彦军   

  1. 西北师范大学数学与统计学院 兰州 730070
  • 收稿日期:2015-04-01 修回日期:2015-11-21 出版日期:2016-02-25 发布日期:2016-02-25
  • 通讯作者: 马巧珍,maqzh@nwnu.edu.cn E-mail:maqzh@nwnu.edu.cn
  • 作者简介:徐玲,13893414055@163.com;张彦军,2003xbsd@163.com
  • 基金资助:

    国家自然科学基金(11101334,11361053);甘肃省自然科学基金(145RJZA112,145RJZA232)和甘肃高校科研项目资助

Asymptotic Behavior of the Solution for the Nonclassical Diffusion Equations with Fading Memory on the Whole Space R3

Ma Qiaozhen, Xu Ling, Zhang Yanjun   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070
  • Received:2015-04-01 Revised:2015-11-21 Online:2016-02-25 Published:2016-02-25
  • Supported by:

    Supported by the NSFC (11101334, 11361053), the NSF of Gansu Province (145RJZA112, 145RJZA232) and the Research Funds of Gansu Universities

摘要:

该文证明了非经典反应扩散方程ututu-∫0k(su(t-s)ds+f(x,u)=g(x)在R3上的全局吸引子的存在性,其中非线性项f(x,u)满足临界条件.

关键词: 非经典反应扩散方程, 衰退记忆, 临界非线性项, 无界区域, 全局吸引子

Abstract:

We prove the existence of global attractors for the nonclassical diffusion equations with fading memory ututu-∫0k(su(t-s)ds+f(x, u)=g(x) defined on the entire space R3, where nonlinearity f(x, u) is critical.

Key words: Nonclassical diffusion equation, Fading memory, Critical nonlinearity, Unbounded domain, Global attractor

中图分类号: 

  • O175.8