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 .

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 Dynamics for the 3D incompressible Navier-Stokes equations with double time delays and damping

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Wei Shi ◽  
Xiaona Cui ◽  
Xuezhi Li ◽  
Xin-Guang Yang
Keyword(s):  
Time Delays ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Pullback Attractors ◽  
Navier Stokes Equations ◽  
Subcritical Nonlinearity ◽  
Double Time ◽  
Autonomous Dynamical Systems

<p style='text-indent:20px;'>This paper is concerned with the tempered pullback attractors for 3D incompressible Navier-Stokes model with a double time-delays and a damping term. The delays are in the convective term and external force, which originate from the control in engineer and application. Based on the existence of weak and strong solutions for three dimensional hydrodynamical model with subcritical nonlinearity, we proved the existence of minimal family for pullback attractors with respect to tempered universes for the non-autonomous dynamical systems.</p>

scholarly journals THREE-DIMENSIONAL SYSTEM OF GLOBALLY MODIFIED NAVIER–STOKES EQUATIONS WITH DELAY

2010 ◽  
Vol 20 (09) ◽  
pp. 2869-2883 ◽  
Author(s):  
TOMÁS CARABALLO ◽  
JOSÉ REAL ◽  
ANTONIO M. MÁRQUEZ
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Pullback Attractor ◽  
Dimensional System ◽  
Navier Stokes Equations ◽  
Three Dimensional System ◽  
Equations With Delay

We prove the existence and uniqueness of strong solutions of a three-dimensional system of globally modified Navier–Stokes equations with delay in the locally Lipschitz case. The asymptotic behavior of solutions, and the existence of pullback attractor are also analyzed.

scholarly journals Upper semicontinuity of pullback attractors for a nonautonomous damped wave equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yonghai Wang ◽  
Minhui Hu ◽  
Yuming Qin
Keyword(s):  
Wave Equation ◽  
Upper Semicontinuity ◽  
Pullback Attractor ◽  
Damped Wave Equation ◽  
Pullback Attractors ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

AbstractIn this paper, we study the local uniformly upper semicontinuity of pullback attractors for a strongly damped wave equation. In particular, under some proper assumptions, we prove that the pullback attractor $\{A_{\varepsilon }(t)\}_{t\in \mathbb{R}}$ { A ε ( t ) } t ∈ R of Eq. (1.1) with $\varepsilon \in [0,1]$ ε ∈ [ 0 , 1 ] satisfies $\lim_{\varepsilon \to \varepsilon _{0}}\sup_{t\in [a,b]} \operatorname{dist}_{H_{0}^{1}\times L^{2}}(A_{\varepsilon }(t),A_{ \varepsilon _{0}}(t))=0$ lim ε → ε 0 sup t ∈ [ a , b ] dist H 0 1 × L 2 ( A ε ( t ) , A ε 0 ( t ) ) = 0 for any $[a,b]\subset \mathbb{R}$ [ a , b ] ⊂ R and $\varepsilon _{0}\in [0,1]$ ε 0 ∈ [ 0 , 1 ] .

scholarly journals Non-autonomous invariant sets and attractors: Random dynamical system

2020 ◽  
Vol 25 (4) ◽  
pp. 17-23
Author(s):  
Mohamedsh Imran ◽  
Ihsan Jabbar Kadhim
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Global Attractors ◽  
Random Dynamical Systems ◽  
Invariant Sets ◽  
Random Dynamical System ◽  
Pullback Attractor ◽  
Pullback Attractors ◽  
Deterministic Dynamical System

 In this paper the concepts of pullback attractor ,pullback absorbing family in (deterministic) dynamical system are defined in (random) dynamical systems. Also some main result such as (existence) of pullback attractors ,upper semi-continuous of pullback attractors and uniform and global attractors are proved in random dynamical system .

Attractor Analysis of Cohen–Grossberg Neural Networks with Multiple Time-Varying Delays

2021 ◽  
Vol 31 (02) ◽  
pp. 2150022
Author(s):  
Li Wan ◽  
Qinghua Zhou
Keyword(s):  
Neural Networks ◽  
Matrix Form ◽  
Pullback Attractor ◽  
Multiple Time ◽  
Time Varying ◽  
Pullback Attractors ◽  
Vector Matrix ◽  
Theoretical Results

This paper investigates the pullback attractor of Cohen–Grossberg neural networks with multiple time-varying delays. Compared with the existing references, the networks considered here are more general and cannot be expressed in the vector-matrix form due to multiple time-varying delays. After constructing a proper Lyapunov–Krasovskii functional and eliminating the terms involving multiple time-varying delays, two sets of new sufficient criteria on the existence of the pullback attractor are derived based on the theory of pullback attractors. In the end, two examples are given to demonstrate the effectiveness of our theoretical results.

scholarly journals Pullback attractors for three-dimensional non-autonomous Navier–Stokes–Voigt equations

Nonlinearity ◽  
2012 ◽  
Vol 25 (4) ◽  
pp. 905-930 ◽  
Author(s):  
Julia García-Luengo ◽  
Pedro Marín-Rubio ◽  
José Real
Keyword(s):  
Three Dimensional ◽  
Navier Stokes ◽  
Pullback Attractors

Pullback attractors for a strongly damped delay wave equation in ℝn

2018 ◽  
Vol 18 (03) ◽  
pp. 1850016
Author(s):  
Yejuan Wang ◽  
Yizhao Qin ◽  
Jingyu Wang
Keyword(s):  
Wave Equation ◽  
Lipschitz Condition ◽  
Unbounded Domain ◽  
Nonlinear Term ◽  
Growth Conditions ◽  
Pullback Attractor ◽  
Pullback Attractors ◽  
New Methods ◽  
Continuity Assumption ◽  
Strongly Damped

In this paper, we prove the existence of a pullback attractor for a strongly damped delay wave equation in [Formula: see text]. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth conditions, so that some new methods to obtain the existence of pullback attractors for multi-valued processes on an unbounded domain are introduced.

Lp-type pullback attractors for a semilinear heat equation on time-varying domains

2015 ◽  
Vol 145 (5) ◽  
pp. 1029-1052 ◽  
Author(s):  
Chunyou Sun ◽  
Yanbo Yuan
Keyword(s):  
Heat Equation ◽  
New Method ◽  
Independent Interest ◽  
Pullback Attractor ◽  
Absorbing Set ◽  
Time Varying ◽  
Asymptotic Decomposition ◽  
Pullback Attractors ◽  
Decomposition Scheme ◽  
Semilinear Heat Equation

We present a new method for investigating the Lp-type pullback attractors (2 ≤ p < ∞) of a semilinear heat equation on a time-varying domain under quite general assumptions on the nonlinear and forcing terms. The existing approach does not appear applicable here as it is impossible to show the existence of a pullback absorbing set in Lp space when p is large. A new asymptotic decomposition scheme for a non-autonomous pullback attractor has been introduced. The abstract results and preliminary lemmas are also of independent interest and applicable to other systems.

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