Dynamical Systems Induced by Continuous Time Difference Equations and Long-time Behavior of Solutions

2003 ◽  
Vol 9 (3-4) ◽  
pp. 263-280 ◽  
Author(s):  
Elena Yu. Romanenko
Keyword(s):  
Dynamical Systems ◽  
Difference Equations ◽  
Continuous Time ◽  
Time Difference ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

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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