On a nonlocal phase-field system

Peter W. Bates; Jianlong Han; Guangyu Zhao

doi:10.1016/j.na.2005.08.013

On a nonlocal phase-field system

Peter W. Bates
, Jianlong Han
, Guangyu Zhao

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

We study the existence, uniqueness and continuous dependence on initial data of the solution to a nonlocal phase-field system on a bounded domain. The system is a gradient flow for a free energy functional with nonlocal interaction. Also we study the asymptotic behavior of the solution and show the existence of an absorbing set in some metric space.

Original language	English
Pages (from-to)	2251-2278
Number of pages	28
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	64
Issue number	10
DOIs	https://doi.org/10.1016/j.na.2005.08.013
State	Published - May 15 2006
Externally published	Yes

ASJC Scopus Subject Areas

Analysis
Applied Mathematics

Keywords

Absorbing set
Long-range interaction
Phase transition

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10.1016/j.na.2005.08.013

Cite this

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title = "On a nonlocal phase-field system",

abstract = "We study the existence, uniqueness and continuous dependence on initial data of the solution to a nonlocal phase-field system on a bounded domain. The system is a gradient flow for a free energy functional with nonlocal interaction. Also we study the asymptotic behavior of the solution and show the existence of an absorbing set in some metric space.",

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T1 - On a nonlocal phase-field system

AU - Bates, Peter W.

AU - Han, Jianlong

AU - Zhao, Guangyu

PY - 2006/5/15

Y1 - 2006/5/15

N2 - We study the existence, uniqueness and continuous dependence on initial data of the solution to a nonlocal phase-field system on a bounded domain. The system is a gradient flow for a free energy functional with nonlocal interaction. Also we study the asymptotic behavior of the solution and show the existence of an absorbing set in some metric space.

AB - We study the existence, uniqueness and continuous dependence on initial data of the solution to a nonlocal phase-field system on a bounded domain. The system is a gradient flow for a free energy functional with nonlocal interaction. Also we study the asymptotic behavior of the solution and show the existence of an absorbing set in some metric space.

KW - Absorbing set

KW - Long-range interaction

KW - Phase transition

UR - https://www.scopus.com/pages/publications/33644900769

UR - https://www.scopus.com/pages/publications/33644900769#tab=citedBy

U2 - 10.1016/j.na.2005.08.013

DO - 10.1016/j.na.2005.08.013

M3 - Article

AN - SCOPUS:33644900769

SN - 0362-546X

VL - 64

SP - 2251

EP - 2278

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 10

ER -

On a nonlocal phase-field system

Abstract

ASJC Scopus Subject Areas

Keywords

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