scholarly journals Uniform attractors of stochastic three-component Gray-Scott system with multiplicative noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Junwei Feng ◽  
Hui Liu ◽  
Jie Xin
Keyword(s):  
Dynamical System ◽  
Bounded Domain ◽  
Multiplicative Noise ◽  
Random Dynamical System ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Long Time ◽  
Uniform Attractors

<p style='text-indent:20px;'>In a bounded domain, we study the long time behavior of solutions of the stochastic three-component Gray-Scott system with multiplicative noise. We first show that the stochastic three-component Gray-Scott system can generate a non-autonomous random dynamical system. Then we establish some uniform estimates of solutions for stochastic three-component Gray-Scott system with multiplicative noise. Finally, the existence of uniform and cocycle attractors is proved.</p>

scholarly journals A Stochastic Weakly Damped, Forced KdV-BO Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Guolian Wang
Keyword(s):  
Dynamical System ◽  
White Noise ◽  
Global Solution ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time ◽  
Energy Type ◽  
Bo Equation

We investigate the long time behavior of the damped, forced KdV-BO equation driven by white noise. We first show that the global solution generates a random dynamical system. By energy type estimates and dispersive properties, we then prove that this system possesses a weak random attractor in the spaceH1(ℝ).

scholarly journals Upper Semicontinuous Property of Uniform Attractors for the 2D Nonautonomous Navier-Stokes Equations with Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Xin-Guang Yang ◽  
Jun-Tao Li
Keyword(s):  
External Force ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Navier Stokes Equations ◽  
Upper Semicontinuous ◽  
Long Time ◽  
Linear Damping ◽  
Uniform Attractors

Our aim is to investigate the long-time behavior in terms of upper semicontinuous property of uniform attractors for the 2D nonautonomous Navier-Stokes equations with linear damping and nonautonomous perturbation external force, that is, the convergence of corresponding attractors when the perturbation tends to zero.

scholarly journals Pullback𝒟-Attractor of Nonautonomous Three-Component Reversible Gray-Scott System on Unbounded Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Anhui Gu
Keyword(s):  
Phase Space ◽  
Global Attractor ◽  
Unbounded Domains ◽  
Time Behavior ◽  
External Forcing ◽  
Long Time Behavior ◽  
Entire Space ◽  
Asymptotic Compactness ◽  
Uniform Estimates ◽  
Long Time

The long time behavior of solutions of the nonautonomous three-components reversible Gray-Scott system defined on the entire spaceℝnis studied when the external forcing terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established inL2ℝn3andH1ℝn3, respectively. The pullback asymptotic compactness of solutions is proved by using uniform estimates on the tails of solutions on unbounded domains.

scholarly journals Reduction of Dynamics with Lie Group Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
M. Iwasa
Keyword(s):  
Dynamical System ◽  
Lie Group ◽  
Perturbation Methods ◽  
Group Analysis ◽  
Lie Symmetries ◽  
Time Behavior ◽  
Lie Group Analysis ◽  
Long Time Behavior ◽  
Singular Perturbation Methods ◽  
Long Time

This paper is mainly a review concerning singular perturbation methods by means of Lie group analysis which has been presented by the author. We make use of a particular type of approximate Lie symmetries in those methods in order to construct reduced systems which describe the long-time behavior of the original dynamical system. Those methods can be used in analyzing not only ordinary differential equations but also difference equations. Although this method has been mainly used in order to derive asymptotic behavior, when we can find exact Lie symmetries, we succeed in construction of exact solutions.

Estimates on the dimension of an exponential attractor for a delay differential equation

2014 ◽  
Vol 64 (5) ◽  
Author(s):  
Sakineh Habibi
Keyword(s):  
Differential Equation ◽  
Fractal Dimension ◽  
Bounded Domain ◽  
Delay Differential Equation ◽  
Exponential Attractor ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time ◽  
Trajectory Method ◽  
Delay Differential

AbstractWe study the long time behavior of delay differential equation, considered in a bounded domain in ℝd. Using the short trajectory method to prove the existence of the exponential attractor. Also we have estimates on the fractal dimension of an exponential attractor.

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