关于全局吸引子的一个新的存在性定理以及它对于非经典扩散方程的应用  

A New Existence Theorem for Global Attractors and its Application to a Non-Classical Di usion Equation

作　　者：QIN Yu-ming CHEN Jia-le JIANG Hui-te 

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

出　　处：《Chinese Quarterly Journal of Mathematics》2023年第3期276-289,共14页数学季刊（英文版）

基　　金：Supported by the NNSF of China(Grant No.12171082);The fundamental research funds for the central universities(Grant Nos.2232022G-13 and 2232023G-13);by a grant from Science and Technology Commission of Shanghai Municipality。

摘　　要：In this paper,we first survey existed theorems and propose all 46 related open problems of the existence of global attractors for autonomous dynamical systems,then establish a new existence theorem of global attractors which will be applied to a nonclassical diffusion equation for the norm-to-weak continuous,weakly compact semigroup on H_(0)^(1)(Ω)and H^(2)(Ω)∩H_(0)^(1)(Ω)respectively.As an application of this new existence theorem of global attractors,we obtain the existence of the global attractors on H_(0)^(1)(Ω)and H^(2)(Ω)∩H_(0)^(1)(Ω)respectively for a nonclassical-diffusion equation.

关 键 词：Nonclassical diffusion equations Norm-to-weak continuity Global attractor 

分 类 号：O193[理学—数学]