Local equi-attraction of pullback attractor sections

2021 ◽  
Vol 494 (2) ◽  
pp. 124657
Author(s):  
Fuzhi Li ◽  
Jie Xin ◽  
Hongyong Cui ◽  
Peter E. Kloeden
Keyword(s):  
Pullback Attractor

Attractors for multi-valued lattice dynamical systems with nonlinear diffusion terms

2021 ◽  
Author(s):  
Panpan Zhang ◽  
Anhui Gu
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Diffusion ◽  
Upper Semicontinuity ◽  
Growth Conditions ◽  
Pullback Attractor ◽  
Random Lattice ◽  
Lipschitz Continuous ◽  
Lattice Dynamical Systems ◽  
Long Term Behavior

This paper is devoted to the long-term behavior of nonautonomous random lattice dynamical systems with nonlinear diffusion terms. The nonlinear drift and diffusion terms are not expected to be Lipschitz continuous but satisfy the continuity and growth conditions. We first prove the existence of solutions, and establish the existence of a multi-valued nonautonomous cocycle. We then show the existence and uniqueness of pullback attractors parameterized by sample parameters. Finally, we establish the measurability of this pullback attractor by the method based on the weak upper semicontinuity of the solutions.

scholarly journals Strong Pullback Attractors of the Nonautonomous Suspension Bridge Equation with Variable Delay

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Suping Wang ◽  
Qiaozhen Ma
Keyword(s):  
Suspension Bridge ◽  
Pullback Attractor ◽  
Variable Delay ◽  
Pullback Attractors ◽  
Time Dynamics ◽  
Multivalued Dynamical Systems ◽  
Delay Effects ◽  
Long Time ◽  
Equations With Delay ◽  
Long Time Dynamics

In this paper, we consider the suspension bridge equation with variable delay. The long-time dynamics of the solutions for the suspension equations without delay effects have been investigated by many authors. But there are few works on suspension equations with delay. Moreover there are not many studies on attractors for other systems with delay. Thus, we study the existence of pullback attractor for the suspension equation with variable delay by using the theory of attractors for multivalued dynamical systems.

scholarly journals The Pullback Attractors for the Nonautonomous Camassa-Holm Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-12
Author(s):  
Delin Wu
Keyword(s):  
Three Dimensional ◽  
Pullback Attractor ◽  
Pullback Attractors

We consider the pullback attractors for the three-dimensional nonautonomous Camassa-Holm equations in the periodic box . Assuming , which is translation bounded, the existence of the pullback attractor for the three-dimensional nonautonomous Camassa-Holm system is proved in and .

On pullback attractor for non-autonomous weakly dissipative wave equations

2009 ◽  
Vol 24 (1) ◽  
pp. 97-108
Author(s):  
Xingjie Yan ◽  
Chengkui Zhong
Keyword(s):  
Wave Equations ◽  
Pullback Attractor

scholarly journals Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Qiuying Lu ◽  
Guifeng Deng ◽  
Weipeng Zhang
Keyword(s):  
Additive Noise ◽  
Dimensional Space ◽  
Landau Equation ◽  
Unbounded Domains ◽  
Random Dynamical System ◽  
Pullback Attractor ◽  
Ginzburg Landau ◽  
Uniform Estimates ◽  
Ginzburg Landau Equation ◽  
Random Attractors

We prove the existence of a pullback attractor inL2(ℝn)for the stochastic Ginzburg-Landau equation with additive noise on the entiren-dimensional spaceℝn. We show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. We demonstrate that the system possesses a uniqueD-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions.

RANDOM ATTRACTORS OF STOCHASTIC REACTION–DIFFUSION EQUATIONS ON VARIABLE DOMAINS

2011 ◽  
Vol 11 (02n03) ◽  
pp. 301-314 ◽  
Author(s):  
H. CRAUEL ◽  
P. E. KLOEDEN ◽  
MEIHUA YANG
Keyword(s):  
Stochastic Partial Differential Equation ◽  
Smooth Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Random Dynamical System ◽  
Pullback Attractor ◽  
Diffusion Type ◽  
Variable Domains ◽  
Reference Domain ◽  
Stochastic Reaction

It is shown that a stochastic partial differential equation of the reaction–diffusion type on time-varying domains obtained by a temporally continuous dependent spatially diffeomorphic transformation of a reference domain, which is bounded with a smooth boundary, generates a "partial-random" dynamical system, which has a pathwise nonautonomous pullback attractor.

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