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

秦玉明, 陈家乐, 姜慧特

doi:10.13371/j.cnki.chin.q.j.m.2023.03.003

数学季刊 >

2023 , Vol. 38 >Issue 3: 276 - 289

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2023.03.003

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

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1. Department of Mathematics, Donghua University, Shanghai 201620, China;
2. Institute for Nonlinear Science, Donghua University, Shanghai 201620, China

QIN Yu-ming (1963-), male, native of Zhengzhou, Henan, professor of Donghua University, Ph.D supervisor, Ph.D, engages in PDE.

网络出版日期: 2023-09-30

基金资助

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

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

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1. Department of Mathematics, Donghua University, Shanghai 201620, China;
2. Institute for Nonlinear Science, Donghua University, Shanghai 201620, China

QIN Yu-ming (1963-), male, native of Zhengzhou, Henan, professor of Donghua University, Ph.D supervisor, Ph.D, engages in PDE.

Online published: 2023-09-30

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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 H01(Ω) and H2(Ω)∩H01(Ω) respectively. As an application of this new existence theorem of global attractors, we obtain the existence of the global attractors onH01(Ω) and H2(Ω)∩ H01(Ω) respectively for a nonclassical-diffusion equation.

关键词： Nonclassical diffusion equations; Norm-to-weak continuity; Global attractor

本文引用格式

秦玉明, 陈家乐, 姜慧特 . 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[J]. 数学季刊, 2023 , 38(3) : 276 -289 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.003

Abstract

Key words： Nonclassical diffusion equations; Norm-to-weak continuity; Global attractor

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