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 H_(0)^(1)(Ω)and H^(2)(Ω)∩H_(0)^(1)(Ω)respectively.As an application of this new existence theorem of global attractors,we obtain the existence of the global attractors on H_(0)^(1)(Ω)and H^(2)(Ω)∩H_(0)^(1)(Ω)respectively for a nonclassical-diffusion equation.
基金
Supported by the NNSF of China(Grant No.12171082)
The fundamental research funds for the central universities(Grant Nos.2232022G-13 and 2232023G-13)
by a grant from Science and Technology Commission of Shanghai Municipality。
