Time-dependent Global Attractors for the Nonclassical Diffusion Equations with Fading Memory  

作　　者：Yu-ming QIN Xiao-ling CHEN 

机构地区：[1]Department of Mathematics,Institute for Nonlinear Science,Donghua University,Shanghai 201620,China [2]Department of Mathematics,Donghua University,Shanghai 201620,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第2期498-512,共15页应用数学学报(英文版)

基　　金：supported by the National Natural Science Foundation of China(No.12171082);the Fundamental Research Funds for the Central Universities(No.2232023G-13).

摘　　要：In this paper,we discuss the long-time behavior of solutions to the nonclassical diffusion equation with fading memory when the nonlinear term f satisfies critical exponential growth and the external force g(x)∈L^(2)(Ω).In the framework of time-dependent spaces,we verify the existence of absorbing sets and the asymptotic compactness of the process,then we obtain the existence of the time-dependent global attractor A={A_(t)g}2R in Mt.Furthermore,we achieve the regularity of A,that is,A_(t) is bounded in M_(t)^(1) with a bound independent of t.

关 键 词：time-dependent global attractors nonclassical diffusion equation fading memory time-dependent spaces long-time behavior 

分 类 号：O175.2[理学—数学]