scholarly journals Pullbackđť’ź-Attractor of Nonautonomous Three-Component Reversible Gray-Scott System on Unbounded Domains

10.1155/2013/719063 â—˝  
2013 â—˝  
Vol 2013 â—˝  
pp. 1-13 â—˝  
Author(s):  
Anhui Gu
Keyword(s):  
Phase Space â—˝  
Global Attractor â—˝  
Unbounded Domains â—˝  
Time Behavior â—˝  
External Forcing â—˝  
Long Time Behavior â—˝  
Entire Space â—˝  
Asymptotic Compactness â—˝  
Uniform Estimates â—˝  
Long Time

The long time behavior of solutions of the nonautonomous three-components reversible Gray-Scott system defined on the entire spaceâ„ťnis studied when the external forcing terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established inL2â„ťn3andH1â„ťn3, respectively. The pullback asymptotic compactness of solutions is proved by using uniform estimates on the tails of solutions on unbounded domains.

Long-Time Behavior for Gradient Parabolic Systems in Some Unbounded Domains

2013 â—˝  
Vol 41 (1) â—˝  
pp. 97-113
Author(s):  
Mai Xuan Thao â—˝  
Vu Manh Toi
Keyword(s):  
Unbounded Domains â—˝  
Parabolic Systems â—˝  
Time Behavior â—˝  
Long Time Behavior â—˝  
Long Time

Effects of phase space discretization on the long-time behavior of dynamical systems

1987 â—˝  
Vol 25 (1-3) â—˝  
pp. 173-180 â—˝  
Author(s):  
C. Beck â—˝  
G. Roepstorff
Keyword(s):  
Phase Space â—˝  
Dynamical Systems â—˝  
Time Behavior â—˝  
Long Time Behavior â—˝  
Long Time â—˝  
Space Discretization

scholarly journals Global Attractor for Doubly Nonlinear Parabolic Equation

10.5402/2012/956291 â—˝  
2012 â—˝  
Vol 2012 â—˝  
pp. 1-16
Author(s):  
Yongjun Li â—˝  
Suyun Wang â—˝  
Yanhong Zhang
Keyword(s):  
Parabolic Equation â—˝  
Global Attractor â—˝  
Parabolic Equations â—˝  
Nonlinear Parabolic Equations â—˝  
Time Behavior â—˝  
Long Time Behavior â—˝  
Nonlinear Parabolic â—˝  
Long Time â—˝  
Doubly Nonlinear â—˝  
Doubly Nonlinear Parabolic Equation

Our aim in this paper is to study the long-time behavior for a class of doubly nonlinear parabolic equations. First we show that the problem has a unique solution. Then we prove that the semigroup corresponding to the problem is norm-to-weak continuous in Lq and H01. Finally we establish the existence of global attractor of the problem in Lq and H01.

scholarly journals Strong Solutions and Global Attractors for Kirchhoff Type Equation

2018 â—˝  
Vol 2018 â—˝  
pp. 1-7
Author(s):  
Xiangping Chen
Keyword(s):  
Phase Space â—˝  
Type Equation â—˝  
Strong Solutions â—˝  
Global Attractors â—˝  
Time Behavior â—˝  
Long Time Behavior â—˝  
Kirchhoff Type â—˝  
Kirchhoff Type Equation â—˝  
Long Time â—˝  
Linear Damping

We study the long-time behavior of the Kirchhoff type equation with linear damping. We prove the existence of strong solution and the semigroup associated with the solution possesses a global attractor in the higher phase space.

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

10.3934/mfc.2021012 â—˝  
2021 â—˝  
Vol 0 (0) â—˝  
pp. 0
Author(s):  
Junwei Feng â—˝  
Hui Liu â—˝  
Jie Xin
Keyword(s):  
Dynamical System â—˝  
Bounded Domain â—˝  
Multiplicative Noise â—˝  
Random Dynamical System â—˝  
Time Behavior â—˝  
Long Time Behavior â—˝  
Uniform Estimates â—˝  
Estimates Of Solutions â—˝  
Long Time â—˝  
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 Pullback attractors via quasi-stability for non-autonomous lattice dynamical systems

2021 â—˝  
Vol 0 (0) â—˝  
pp. 0
Author(s):  
Radosław Czaja
Keyword(s):  
Dynamical Systems â—˝  
Global Attractor â—˝  
Exponential Attractor â—˝  
Time Behavior â—˝  
Long Time Behavior â—˝  
Pullback Attractors â—˝  
Diffusion Operator â—˝  
First Order â—˝  
Lattice Dynamical Systems â—˝  
Long Time

<p style='text-indent:20px;'>In this paper we study long-time behavior of first-order non-autono-mous lattice dynamical systems in square summable space of double-sided sequences using the cooperation between the discretized diffusion operator and the discretized reaction term. We obtain existence of a pullback global attractor and construct pullback exponential attractor applying the introduced notion of quasi-stability of the corresponding evolution process.</p>

scholarly journals Global attractor for a class of nonlinear generalized Kirchhoff models

2016 â—˝  
Vol 12 (8) â—˝  
pp. 6452-6462 â—˝  
Author(s):  
Penghui Lv â—˝  
Jingxin Lu â—˝  
Guoguang Lin
Keyword(s):  
Boundary Value Problem â—˝  
Global Attractor â—˝  
Initial Boundary â—˝  
Initial Boundary Value Problem â—˝  
Well Posedness â—˝  
Time Behavior â—˝  
Long Time Behavior â—˝  
Natural Energy â—˝  
Long Time â—˝  
Initial Boundary Value

The paper studies the long time behavior of solutions to the initial boundary value problem(IBVP) for a class of Kirchhoff models flow  .We establish the well-posedness, theexistence of the global attractor in natural energy space

GLOBAL BIFURCATION AND LONG TIME BEHAVIOR OF THE VOLTERRA–LOTKA ECOLOGICAL MODEL

2001 â—˝  
Vol 11 (01) â—˝  
pp. 133-142 â—˝  
Author(s):  
KAITAI LI â—˝  
LIZHOU WANG
Keyword(s):  
Steady State â—˝  
Global Attractor â—˝  
Ecological Model â—˝  
Global Bifurcation â—˝  
Time Behavior â—˝  
Order Interval â—˝  
Long Time Behavior â—˝  
Positive Steady State â—˝  
Long Time â—˝  
Steady State Solutions

The structure of the positive steady-state solutions for the Volterra–Lotka ecological model of two cooperating species is investigated. Some new results of existence, nonexistence and uniqueness are presented. The existence of a global attractor which is contained in an order interval is shown and the bounds of various dimensions of the attractor are given.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 â—˝  
Vol 2020 (1) â—˝  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary â—˝  
Initial Boundary Value Problem â—˝  
Global Dynamics â—˝  
Time Behavior â—˝  
Long Time Behavior â—˝  
Initial Value â—˝  
Hilliard Equation â—˝  
Long Time â—˝  
Cahn Hilliard Equation â—˝  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

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