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

QIN Yu-ming, CHEN Jia-le, JIANG Hui-te

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

Chinese Quarterly Journal of Mathematics >

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

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

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

Supported by

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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Abstract

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.

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

Cite this article

QIN Yu-ming, CHEN Jia-le, JIANG Hui-te . A New Existence Theorem for Global Attractors and its Application to a Non-Classical Diffusion Equation[J]. Chinese Quarterly Journal of Mathematics, 2023 , 38(3) : 276 -289 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.003

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