Chinese Quarterly Journal of Mathematics ›› 2023, Vol. 38 ›› Issue (3): 276-289.doi: 10.13371/j.cnki.chin.q.j.m.2023.03.003

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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.

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

CLC Number: