scholarly journals Backwards Asymptotically Autonomous Dynamics for 2D MHD Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Jiali Yu ◽  
Wenhuo Su ◽  
Dongmei Xu
Keyword(s):  
Topological Property ◽  
Existence Result ◽  
Mhd Equations ◽  
Pullback Attractors

We consider the backwards topological property of pullback attractors for the nonautonomous MHD equations. Under some backwards assumptions of the nonautonomous force, it is shown that the theoretical existence result for such an attractor is derived from an increasing, bounded pullback absorbing and the backwards pullback flattening property. Meanwhile, some abstract results on the convergence of nonautonomous pullback attractors in asymptotically autonomous problems are established and applied to MHD equations.

scholarly journals Pullback attractors of the Jeffreys–Oldroyd equations

2016 ◽  
Vol 260 (6) ◽  
pp. 5026-5042 ◽  
Author(s):  
Victor Zvyagin ◽  
Stanislav Kondratyev
Keyword(s):  
Pullback Attractors

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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