Taiwanese Journal of Mathematics


Kunimochi Sakamoto

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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.

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

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

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

curvature flow minimal surface reaction-diffusion equation


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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