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非经典扩散方程的拉回吸引子在H_0-1(Ω)中的上半连续性

Upper Semicontinuity of Pullback Attractors for Nonclassical Diffusion Equations in H_0-1(Ω)
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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H_01(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,ε_0∈[0,1]满足limε→ε_0 sup t∈[a,b] dist_H_01(Ω)(A_ε(t),A_(ε_0)(t))=0,并且集合∪_(t∈[a,b])∪_(ε∈[0,1])A_ε(t)是H_01(Ω)中的紧集. 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 ε_0 ∈[0,1],limε→ε_0 sup t∈[a,b] dist_(H_01)(A_ε(t),A_ε_0(t)) = 0and ∪_(t∈[a,.b])∪_(ε∈[0,1]) A_ε(t) is precompact in H_0-1(Ω).
出处 《数学物理学报(A辑)》 CSCD 北大核心 2016年第5期946-957,共12页 Acta Mathematica Scientia
基金 国家自然科学基金(11501096 11271066) 中央高校基本科研业务费专项资金(2232015D3-36)资助~~
关键词 拉回吸引子 上半连续性 非经典扩散方程 Pullback attractor Upper semicontinuity Nonclassical diffusion equation
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