A further study on the coupled Allen–Cahn/Cahn–Hilliard equations

Abstract In this paper, we will show that solutions of the initial boundary value problem for the coupled system of Allen–Cahn/Cahn–Hilliard equations continuously depend on parameters of the system, and under some restrictions on the parameters all solutions of the initial boundary value problem fo...

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Main Authors:	Jiaqi Yang, Changchun Liu
Format:	Article
Language:	English
Published:	SpringerOpen 2019-03-01
Series:	Boundary Value Problems
Subjects:	Decay estimate Continuous dependence Allen–Cahn/Cahn–Hilliard equations
Online Access:	http://link.springer.com/article/10.1186/s13661-019-1166-4

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spelling	doaj-6bf28e043ac34af585e1680cb50309842020-11-25T03:32:28ZengSpringerOpenBoundary Value Problems1687-27702019-03-012019111410.1186/s13661-019-1166-4A further study on the coupled Allen–Cahn/Cahn–Hilliard equationsJiaqi Yang0Changchun Liu1Department of Mathematics, Jilin UniversityDepartment of Mathematics, Jilin UniversityAbstract In this paper, we will show that solutions of the initial boundary value problem for the coupled system of Allen–Cahn/Cahn–Hilliard equations continuously depend on parameters of the system, and under some restrictions on the parameters all solutions of the initial boundary value problem for Allen–Cahn/Cahn–Hilliard equations tend to zero with an exponential rate as t→∞ $t\rightarrow\infty$.http://link.springer.com/article/10.1186/s13661-019-1166-4Decay estimateContinuous dependenceAllen–Cahn/Cahn–Hilliard equations
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jiaqi Yang Changchun Liu
spellingShingle	Jiaqi Yang Changchun Liu A further study on the coupled Allen–Cahn/Cahn–Hilliard equations Boundary Value Problems Decay estimate Continuous dependence Allen–Cahn/Cahn–Hilliard equations
author_facet	Jiaqi Yang Changchun Liu
author_sort	Jiaqi Yang
title	A further study on the coupled Allen–Cahn/Cahn–Hilliard equations
title_short	A further study on the coupled Allen–Cahn/Cahn–Hilliard equations
title_full	A further study on the coupled Allen–Cahn/Cahn–Hilliard equations
title_fullStr	A further study on the coupled Allen–Cahn/Cahn–Hilliard equations
title_full_unstemmed	A further study on the coupled Allen–Cahn/Cahn–Hilliard equations
title_sort	further study on the coupled allen–cahn/cahn–hilliard equations
publisher	SpringerOpen
series	Boundary Value Problems
issn	1687-2770
publishDate	2019-03-01
description	Abstract In this paper, we will show that solutions of the initial boundary value problem for the coupled system of Allen–Cahn/Cahn–Hilliard equations continuously depend on parameters of the system, and under some restrictions on the parameters all solutions of the initial boundary value problem for Allen–Cahn/Cahn–Hilliard equations tend to zero with an exponential rate as t→∞ $t\rightarrow\infty$.
topic	Decay estimate Continuous dependence Allen–Cahn/Cahn–Hilliard equations
url	http://link.springer.com/article/10.1186/s13661-019-1166-4
work_keys_str_mv	AT jiaqiyang afurtherstudyonthecoupledallencahncahnhilliardequations AT changchunliu afurtherstudyonthecoupledallencahncahnhilliardequations AT jiaqiyang furtherstudyonthecoupledallencahncahnhilliardequations AT changchunliu furtherstudyonthecoupledallencahncahnhilliardequations
_version_	1724568086408855552

A further study on the coupled Allen–Cahn/Cahn–Hilliard equations

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