数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1205-1223.

• 论文 • 上一篇    下一篇

记忆型非经典扩散方程在 H1(Rn) x Lu2(R+;H1(Rn))中的全局吸引子

汪璇*(),韩英(),高承华()   

  1. 西北师范大学数学与统计学院 兰州 730070
  • 收稿日期:2017-07-17 出版日期:2018-12-26 发布日期:2018-12-27
  • 通讯作者: 汪璇 E-mail:wangxuan@nwnu.edu.cn;469328224@qq.com;gaochenghua@nwnu.edu.cn
  • 作者简介:韩英, E-mail:469328224@qq.com|高承华, E-mail:gaochenghua@nwnu.edu.cn
  • 基金资助:
    国家自然科学基金(11761062);国家自然科学基金(11561064);国家自然科学基金(11661071);西北师范大学青年教师科研能力提升计划(NWNU-LKQN-14-6);甘肃省高校科研项目(2016A-003)

Global Attractor in H1(Rn) x Lu2(R+;H1(Rn)) for the Nonclassical Diffusion Equations with Fading Memory

Xuan Wang*(),Ying Han(),Chenghua Gao()   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070
  • Received:2017-07-17 Online:2018-12-26 Published:2018-12-27
  • Contact: Xuan Wang E-mail:wangxuan@nwnu.edu.cn;469328224@qq.com;gaochenghua@nwnu.edu.cn
  • Supported by:
    the NSFC(11761062);the NSFC(11561064);the NSFC(11661071);the Young Teachers Scientific Research Ability Promotion Plan of Northwest Normal University(NWNU-LKQN-14-6);the Science Research Project for Colleges and Universities of Gansu Province(2016A-003)

摘要:

该文研究了带有衰退记忆和超临界非线性项的非经典扩散方程在无界域Rn中的动力学行为.运用半群理论和收缩函数方法,当外力项仅属于H-1Rn)时,证明了全局吸引子在H1(Rn)×L2μ(R+;H1(Rn))中的存在性.

关键词: 非经典扩散方程, 衰退记忆, 收缩函数, 全局吸引子

Abstract:

In this paper, we are concerned with the dynamical behavior of the nonclassical diffusion equations with fading memory and supercritical nonlinearity on unbounded domain Rn. By applying semigroup theory and method of contractive function, we obtain the existence of global attractors in H1(Rn)×L2μ(R+;H1(Rn)), when the external forcing term g merely belongs to H-1(Rn).

Key words: Nonclassical diffusion equation, Fading memory, Contractive function, Global attractor

中图分类号: 

  • O175.8