非经典扩散方程的拉回吸引子在H01(Ω)中的上半连续性

数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 946-957.

非经典扩散方程的拉回吸引子在H₀¹(Ω)中的上半连续性

汪永海, 秦玉明

东华大学理学院应用数学系上海 201620

收稿日期:2015-12-25 修回日期:2016-06-07 出版日期:2016-10-26 发布日期:2016-10-26
作者简介:汪永海,E-mail:yonghai@dhu.edu.cn
基金资助:
国家自然科学基金（11501096，11271066）和中央高校基本科研业务费专项资金（2232015D3-36）资助

Upper Semicontinuity of Pullback Attractors for Nonclassical Diffusion Equations in H₀¹(Ω)

Wang Yonghai, Qin Yuming

Department of Applied Mathematics, Donghua University

Received:2015-12-25 Revised:2016-06-07 Online:2016-10-26 Published:2016-10-26
Supported by:
Supported by the NSFC(11501096, 11271066) and the Fundamental Research Funds for the Central Universities (2232015D3-36)

摘要/Abstract

摘要：

该文主要考虑一类非线性项具有临界指数增长的非自治非经典扩散方程生成的拉回吸引子在H₀¹(Ω)空间中的上半连续性.具体来讲，该文讨论了方程（1.1）生成的拉回吸引子{A_ε(t)}_t∈R(ε∈[0，1])，对任意的[a，b]⊂R，ε₀∈[0，1]满足dist_H₀¹(Ω)(A_ε(t)，A_ε₀(t))=0，]并且集合∪_t∈[a，b]∪_ε∈[0，1]A_ε(t)是H₀¹(Ω)中的紧集.

关键词: 拉回吸引子, 上半连续性, 非经典扩散方程

Abstract:

This paper is concerned with upper semicontinuity of pullback attractors, for a nonautonomous nonclassical diffusion equation with critical nonlinearity. In particular, under some proper assumptions, we prove that, the pullback attractor {A_ε(t)}_t∈R of equation (1.1) with ε∈[0,1] satisfies that for any [a,b]⊂R and ε₀∈[0,1], dist_H₀¹(A_ε(t),A_ε₀(t))=0 and ∪_t∈[a,b]∪_ε∈[0,1]A_ε(t) is precompact in H₀¹(Ω).

Key words: Pullback attractor, Upper semicontinuity, Nonclassical diffusion equation

中图分类号:

O175

汪永海, 秦玉明. 非经典扩散方程的拉回吸引子在H₀¹(Ω)中的上半连续性[J]. 数学物理学报, 2016, 36(5): 946-957.

Wang Yonghai, Qin Yuming. Upper Semicontinuity of Pullback Attractors for Nonclassical Diffusion Equations in H₀¹(Ω)[J]. Acta mathematica scientia,Series A, 2016, 36(5): 946-957.

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非经典扩散方程的拉回吸引子在H₀¹(Ω)中的上半连续性

Upper Semicontinuity of Pullback Attractors for Nonclassical Diffusion Equations in H₀¹(Ω)

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