Existence and global stability of traveling curved fronts in the Allen-Cahn equations

Hirokazu Ninomiya; Masaharu Taniguchi

doi:10.1016/j.jde.2004.06.011

Existence and global stability of traveling curved fronts in the Allen-Cahn equations

Hirokazu Ninomiya, Masaharu Taniguchi

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

114 Citations (Scopus)

Abstract

This paper is concerned with existence and stability of traveling curved fronts for the Allen-Cahn equation in the two-dimensional space. By using the supersolution and the subsolution, we construct a traveling curved front, and show that it is the unique traveling wave solution between them. Our supersolution can be taken arbitrarily large, which implies some global asymptotic stability for the traveling curved front.

Original language	English
Pages (from-to)	204-233
Number of pages	30
Journal	Journal of Differential Equations
Volume	213
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2004.06.011
Publication status	Published - Jun 1 2005
Externally published	Yes

Keywords

Allen-Cahn equation
Curved front
Stability
Traveling wave

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2004.06.011

Cite this

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abstract = "This paper is concerned with existence and stability of traveling curved fronts for the Allen-Cahn equation in the two-dimensional space. By using the supersolution and the subsolution, we construct a traveling curved front, and show that it is the unique traveling wave solution between them. Our supersolution can be taken arbitrarily large, which implies some global asymptotic stability for the traveling curved front.",

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AB - This paper is concerned with existence and stability of traveling curved fronts for the Allen-Cahn equation in the two-dimensional space. By using the supersolution and the subsolution, we construct a traveling curved front, and show that it is the unique traveling wave solution between them. Our supersolution can be taken arbitrarily large, which implies some global asymptotic stability for the traveling curved front.

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KW - Curved front

KW - Stability

KW - Traveling wave

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Existence and global stability of traveling curved fronts in the Allen-Cahn equations

Abstract

Keywords

ASJC Scopus subject areas

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