scholarly journals Long-time behavior of solution and semi-discrete scheme for one nonlinear parabolic integro-differential equation

2016 ◽  
Vol 170 (1) ◽  
pp. 47-55 ◽  
Author(s):  
Temur Jangveladze
Keyword(s):  
Differential Equation ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Integro Differential Equation ◽  
Discrete Scheme ◽  
Nonlinear Parabolic ◽  
Long Time

scholarly journals Global Attractor for Doubly Nonlinear Parabolic Equation

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

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.

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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