Transition layers for a spatially inhomogeneous Allen-Cahn equation in multi-dimensional domains | Zendy

Fang Li | Zendy; Kimie Nakashima | Zendy

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Transition layers for a spatially inhomogeneous Allen-Cahn equation in multi-dimensional domains

Author(s) -

Fang Li,

Kimie Nakashima

Publication year - 2011

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2012.32.1391

Subject(s) - hypersurface , omega , allen–cahn equation , domain (mathematical analysis) , physics , mathematical analysis , transition (genetics) , mathematical physics , mathematics , materials science , condensed matter physics , chemistry , quantum mechanics , biochemistry , gene

In this paper, we study a spatially inhomogeneous Allen-Cahn equation in multi-dimensional domains. By upper and lower solution method, we obtain a sufficient condition for a hypersurface $S$ in the domain $\Omega$ to support stable transition layers, and a necessary condition for $S$ in $\Omega$ to support transition layers, not necessarily stable. In addition, sharp estimates on depths of transition layers have also been derived.

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