Upper semicontinuity of pullback attractors for nonclassical diffusion equations

2010 ◽  
Vol 51 (2) ◽  
pp. 022701 ◽  
Author(s):  
Yonghai Wang ◽  
Yuming Qin
Keyword(s):  
Upper Semicontinuity ◽  
Diffusion Equations ◽  
Pullback Attractors ◽  
Nonclassical Diffusion Equations

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.

scholarly journals Upper semicontinuity of attractors for nonclassical diffusion equations with arbitrary polynomial growth

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yongqin Xie ◽  
Jun Li ◽  
Kaixuan Zhu
Keyword(s):  
Polynomial Growth ◽  
A Priori ◽  
Upper Semicontinuity ◽  
A Priori Estimate ◽  
Global Attractors ◽  
Diffusion Equations ◽  
Nonlinear Anal ◽  
Estimate Method ◽  
Appl Math ◽  
Nonclassical Diffusion Equations

AbstractIn this paper, we mainly investigate upper semicontinuity and regularity of attractors for nonclassical diffusion equations with perturbed parameters ν and the nonlinear term f satisfying the polynomial growth of arbitrary order $p-1$ p − 1 ($p \geq 2$ p ≥ 2 ). We extend the asymptotic a priori estimate method (see (Wang et al. in Appl. Math. Comput. 240:51–61, 2014)) to verify asymptotic compactness and upper semicontinuity of a family of semigroups for autonomous dynamical systems (see Theorems 2.2 and 2.3). By using the new operator decomposition method, we construct asymptotic contractive function and obtain the upper semicontinuity for our problem, which generalizes the results obtained in (Wang et al. in Appl. Math. Comput. 240:51–61, 2014). In particular, the regularity of global attractors is obtained, which extends and improves some results in (Xie et al. in J. Funct. Spaces 2016:5340489, 2016; Xie et al. in Nonlinear Anal. 31:23–37, 2016).

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