ANALYSIS OF A GENERALIZED LANGEVIN EQUATION WITH FRACTIONAL DERIVATIVE, NONLOCAL DISSIPATIVE FORCE AND LINEAR EXTERNAL FORCE

2008 ◽  
Vol 08 (03n04) ◽  
pp. L381-L391 ◽  
Author(s):  
KWOK SAU FA
Keyword(s):  
Fractional Derivative ◽  
External Force ◽  
Langevin Equation ◽  
Relaxation Function ◽  
Dissipative Force ◽  
Generalized Langevin Equation ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Memory Kernel ◽  
Long Time

We analyze the motion of a particle governed by a generalized Langevin equation with fractional derivative, nonlocal dissipative force and linear external force. We consider the dissipative memory kernel given by the exponential and power-law functions. For these cases, one can obtain exact results for the relaxation function. The long-time behavior of this function is also investigated. Our results show that the inertial term has no significant influence on the long-time behavior.

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 Approximate Kelvin-Voigt Fluid Driven by an External Force Depending on Velocity with Distributed Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yantao Guo ◽  
Shuilin Cheng ◽  
Yanbin Tang
Keyword(s):  
External Force ◽  
Distributed Delay ◽  
Navier Stokes ◽  
Pullback Attractor ◽  
Sufficient Condition ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Prior Estimate ◽  
Long Time ◽  
Voigt Fluid

We consider the approximate 3D Kelvin-Voigt fluid driven by an external force depending on velocity with distributed delay. We investigate the long time behavior of solutions to Navier-Stokes-Voigt equation with a distributed delay external force depending on the velocity of fluid on a bounded domain. By a prior estimate and a contractive function, we give a sufficient condition for the existence of pullback attractor of NSV equation.

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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