数学物理学报 ›› 2015, Vol. 35 ›› Issue (4): 641-650.

• 论文 •    下一篇

反应扩散方程在H2(Ω)和L2P-2(Ω)中的指数吸引子

王刚1, 汤燕斌2   

  1. 1 湖北工业大学理学院, 武汉 430068;
    2 华中科技大学数学与统计学院, 武汉 430074
  • 收稿日期:2014-02-28 修回日期:2015-03-17 出版日期:2015-08-25 发布日期:2015-08-25
  • 作者简介:王刚, wgfeiyu@sina.com;汤燕斌, tangybhust@sina.com
  • 基金资助:

    国家自然科学基金(11471129)资助

Exponential Attractors for Reaction-Diffusion Equations in H2(Ω) and L2P-2(Ω)

Wang Gang1, Tang Yanbin2   

  1. 1 School of Sciences, Hubei University of Technology, Wuhan 430068;
    2 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074
  • Received:2014-02-28 Revised:2015-03-17 Online:2015-08-25 Published:2015-08-25

摘要:

该文讨论一类具有任意多项式增长非线性项和非齐次项的反应扩散方程指数吸引子的存在性. 首先, 对R3中的有界开子集Ω, 分别选取解半群 S(t)在L2(Ω)和H2(Ω)中的有界正不变吸收集来构造 H2(Ω)中的指数吸引子. 然后证明对某个足够大的时间T1, S(T1) 在这两个吸收集之间是Lipschitz连续的. 最后由一种新的逼近技 巧证明了对任意的g∈ L2(Ω), S(t)在L2P-2(Ω) 中存在指数吸引子. 该结论推广了已有文献中的结果.

关键词: 指数吸引子, 反应扩散方程, Lipschitz连续性

Abstract:

A class of reaction-diffusion equations with arbitrary polynomial growth nonlinearity f and nonhomogeneous term g are concerned in this paper. We first construct exponential attractors in H2(Ω) for the underlying semigroup when Ω is a bounded open set in R3. We obtain this result by proving the Lipschitz continuity between some positively invariant absorbing set in L2(Ω) and some positively invariant absorbing set in H2(Ω). Then, we obtain exponential attractors in L2P-2(Ω) for any gL2(Ω) by using a new approaching technique. This improves the result in previous references.

Key words: Exponential attractors, Reaction-diffusion equations, Lipschitz continuity

中图分类号: 

  • O175.2