Uniform Attractors of Nonclassical Diffusion Equations Lacking Instantaneous Damping on $\mathbb{R}^{N}$ with Memory

2020 ◽  
Vol 170 (1) ◽  
pp. 789-822
Author(s):  
Nguyen Duong Toan
Keyword(s):  
Diffusion Equations ◽  
Uniform Attractors ◽  
With Memory ◽  
Nonclassical Diffusion Equations

scholarly journals Uniform Attractors for Nonclassical Diffusion Equations with Memory

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Yongqin Xie ◽  
Yanan Li ◽  
Ye Zeng
Keyword(s):  
Polynomial Growth ◽  
Arbitrary Order ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Fading Memory ◽  
Uniform Attractor ◽  
Nonclassical Diffusion Equation ◽  
Uniform Attractors ◽  
With Memory ◽  
Nonclassical Diffusion Equations

We introduce a new method (or technique), asymptotic contractive method, to verify uniform asymptotic compactness of a family of processes. After that, the existence and the structure of a compact uniform attractor for the nonautonomous nonclassical diffusion equation with fading memory are proved under the following conditions: the nonlinearityfsatisfies the polynomial growth of arbitrary order and the time-dependent forcing termgis only translation-bounded inLloc2(R;L2(Ω)).

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