scholarly journals Attractors for the Nonclassical Diffusion Equations with Fading Memory and White Noise

2020 ◽  
Vol 7 (9) ◽  
pp. 197-207
Author(s):  
Haihua Luo ◽  
Xianyun Du
Keyword(s):  
White Noise ◽  
Diffusion Equations ◽  
Fading 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)).

Existence and regularity of time-dependent pullback attractors for the non-autonomous nonclassical diffusion equations

2021 ◽  
pp. 1-18
Author(s):  
Yuming Qin ◽  
Bin Yang
Keyword(s):  
Weak Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Diffusion ◽  
Force Term ◽  
Pullback Attractors ◽  
Critical Exponential Growth ◽  
Nonclassical Diffusion Equations

In this paper, we prove the existence and regularity of pullback attractors for non-autonomous nonclassical diffusion equations with nonlocal diffusion when the nonlinear term satisfies critical exponential growth and the external force term $h \in L_{l o c}^{2}(\mathbb {R} ; H^{-1}(\Omega )).$ Under some appropriate assumptions, we establish the existence and uniqueness of the weak solution in the time-dependent space $\mathcal {H}_{t}(\Omega )$ and the existence and regularity of the pullback attractors.

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