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