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

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

scholarly journals Strong Solutions and Global Attractors for Kirchhoff Type Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xiangping Chen
Keyword(s):  
Phase Space ◽  
Type Equation ◽  
Strong Solutions ◽  
Global Attractors ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Long Time ◽  
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 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 Pullback attractors via quasi-stability for non-autonomous lattice dynamical systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Radosław Czaja
Keyword(s):  
Dynamical Systems ◽  
Global Attractor ◽  
Exponential Attractor ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Pullback Attractors ◽  
Diffusion Operator ◽  
First Order ◽  
Lattice Dynamical Systems ◽  
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 On global dynamics of 2D convective Cahn–Hilliard equation

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

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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