数学季刊 ›› 2023, Vol. 38 ›› Issue (3): 276-289.doi: 10.13371/j.cnki.chin.q.j.m.2023.03.003

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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

  

  1. 1. Department of Mathematics, Donghua University, Shanghai 201620, China;
    2. Institute for Nonlinear Science, Donghua University, Shanghai 201620, China
  • 出版日期:2023-09-30 发布日期:2023-09-30
  • 通讯作者: QIN Yu-ming (1963-), male, native of Zhengzhou, Henan, professor of Donghua University, Ph.D supervisor, Ph.D, engages in PDE. E-mail:yuming qin@hotmail.com
  • 作者简介:QIN Yu-ming (1963-), male, native of Zhengzhou, Henan, professor of Donghua University, Ph.D supervisor, Ph.D, engages in PDE.
  • 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.

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

  1. 1. Department of Mathematics, Donghua University, Shanghai 201620, China;
    2. Institute for Nonlinear Science, Donghua University, Shanghai 201620, China
  • Online:2023-09-30 Published:2023-09-30
  • Contact: QIN Yu-ming (1963-), male, native of Zhengzhou, Henan, professor of Donghua University, Ph.D supervisor, Ph.D, engages in PDE. E-mail:yuming qin@hotmail.com
  • About author:QIN Yu-ming (1963-), male, native of Zhengzhou, Henan, professor of Donghua University, Ph.D supervisor, Ph.D, engages in PDE.
  • 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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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

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

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