Taiwanese Journal of Mathematics

EXISTENCE AND STABILITY OF THREE-DIMENSIONAL BOUNDARY-INTERIOR LAYERS FOR THE ALLEN-CAHN EQUATION

Kunimochi Sakamoto

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Abstract

A minimal surface intersecting the boundary of a smooth bounded domain $\subset\mathbb{R}^3$, when it is non-degenerate, gives rise to a family of transition layer solutions of the Allen-Cahn equation. The stability properties of the transition layer solution are determined by the eigenvalues of the Jacobi operator on the minimal surface with Robin type boundary conditions which encode the geometric information of the domain boundary.

Article information

Source
Taiwanese J. Math., Volume 9, Number 3 (2005), 331-358.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407844

Digital Object Identifier
doi:10.11650/twjm/1500407844

Mathematical Reviews number (MathSciNet)
MR2162881

Zentralblatt MATH identifier
1090.35024

Subjects
Primary: 35K57: Reaction-diffusion equations 35J25: Boundary value problems for second-order elliptic equations 35B25: Singular perturbations 58J32: Boundary value problems on manifolds

Keywords
curvature flow minimal surface reaction-diffusion equation

Citation

Sakamoto, Kunimochi. EXISTENCE AND STABILITY OF THREE-DIMENSIONAL BOUNDARY-INTERIOR LAYERS FOR THE ALLEN-CAHN EQUATION. Taiwanese J. Math. 9 (2005), no. 3, 331--358. doi:10.11650/twjm/1500407844. https://projecteuclid.org/euclid.twjm/1500407844


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