Existence and stability of three-dimensional boundary-interior layers for the Allen-Cahn equation (Q812858)
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scientific article; zbMATH DE number 5001896
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence and stability of three-dimensional boundary-interior layers for the Allen-Cahn equation |
scientific article; zbMATH DE number 5001896 |
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Existence and stability of three-dimensional boundary-interior layers for the Allen-Cahn equation (English)
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26 January 2006
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The author deals with the transition-layer solutions to the Allen-Cahn equation in a smooth bounded domain in \(\mathbb R^3\). 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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Curvature flow
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Minimal surface
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Reaction-diffusion equation
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transition-layer solutions
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