scholarly journals PULLBACK ATTRACTOR FOR A NON-AUTONOMOUS GENERALIZED CAHN-HILLIARD EQUATION WITH BIOLOGICAL APPLICATIONS

2016 ◽  
Vol 21 (3) ◽  
pp. 371-384
Author(s):  
Ning Duan
Keyword(s):  
External Force ◽  
Exponential Growth ◽  
Pullback Attractor ◽  
Biological Applications ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

In this paper, we consider a non-autonomous generalized Cahn-Hilliard equation with biological applications. It is shown that a pullback attractor of the equation exists when the external force has exponential growth.

scholarly journals Random Pullback Attractor of a Non-autonomous Local Modified Stochastic Swift-Hohenberg with Multiplicative Noise

2020 ◽  
Author(s):  
Yongjun Li ◽  
Tinggang Zhao ◽  
Hongqing Wu
Keyword(s):  
External Force ◽  
Exponential Growth ◽  
Multiplicative Noise ◽  
Pullback Attractor ◽  
Stochastic Term

In this paper, we study the existence of the random -pullback attractor of a non-autonomous local modified stochastic Swift-Hohenberg equation with multiplicative noise in stratonovich sense. It is shown that a random -pullback attractor exists in when its external force has exponential growth. Due to the stochastic term, the estimate are delicate, we overcome this difficulty by using the Ornstein-Uhlenbeck(O-U) transformation and its properties.

PHASE SEPARATION DYNAMICS AND EXTERNAL FORCE FIELD

1988 ◽  
Vol 02 (06) ◽  
pp. 765-771 ◽  
Author(s):  
K. KITAHARA ◽  
Y. OONO ◽  
DAVID JASNOW
Keyword(s):  
Dynamical System ◽  
Phase Separation ◽  
Force Field ◽  
External Force ◽  
System Modeling ◽  
Bulk Phase ◽  
Hilliard Equation ◽  
External Force Field ◽  
Dynamical System Modeling ◽  
Cahn Hilliard Equation

If spinodal decomposition is modeled by the Cahn-Hilliard (-Cook) equation, the effect of a uniform external force such as gravitation does not appear in the bulk phase kinetics. In contrast, in the Kawasaki exchange modeling of the local dynamics of binary alloys, this effect directly modifies the bulk phase kinetics. We resolve this paradox through the cell-dynamical-system modeling of the Kawasaki exchange dynamics. Its continuum version has turned out to be a modified Cahn-Hilliard equation already proposed by Langer et al. about ten years ago. We demonstrate some examples in which the correction to the Cahn-Hilliard equation is significant.

scholarly journals On a generalized Cahn-Hilliard equation with biological applications

2014 ◽  
Vol 19 (7) ◽  
pp. 2013-2026 ◽  
Author(s):  
Laurence Cherfils ◽  
◽  
Alain Miranville ◽  
Sergey Zelik ◽  
◽  
...  
Keyword(s):  
Biological Applications ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

scholarly journals On the Cahn-Hilliard equation with mass source for biological applications

2020 ◽  
Vol 0 (0) ◽  
pp. 1-16
Author(s):  
Hussein Fakih ◽  
◽  
Ragheb Mghames ◽  
Noura Nasreddine ◽  
◽  
...  
Keyword(s):  
Biological Applications ◽  
Mass Source ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

scholarly journals On the sharp interface limit of a model for phase separation on biological membranes

Analysis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Helmut Abels ◽  
Johannes Kampmann
Keyword(s):  
Lipid Raft ◽  
Cell Membranes ◽  
System Modeling ◽  
Bulk Diffusion ◽  
Type Equation ◽  
Sharp Interface ◽  
Interface Problem ◽  
Hilliard Equation ◽  
System A ◽  
Cahn Hilliard Equation

AbstractWe rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed in [H. Garcke, J. Kampmann, A. Rätz and M. Röger, A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes, Math. Models Methods Appl. Sci. 26 2016, 6, 1149–1189] to weak (varifold) solutions of the corresponding sharp-interface problem for a suitable subsequence. In the system a Cahn–Hilliard type equation on the boundary of a domain is coupled to a diffusion equation inside the domain. The proof builds on techniques developed in [X. Chen, Global asymptotic limit of solutions of the Cahn–Hilliard equation, J. Differential Geom. 44 1996, 2, 262–311] for the corresponding result for the Cahn–Hilliard 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 ) .

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