Stationary solutions for the Cahn-Hilliard equation (Q1265751)
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scientific article; zbMATH DE number 1202592
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stationary solutions for the Cahn-Hilliard equation |
scientific article; zbMATH DE number 1202592 |
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Stationary solutions for the Cahn-Hilliard equation (English)
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7 April 1999
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The Cahn-Hilliard equation is an accepted macroscopic field-theoretical model of processes such as phase separation in a binary alloy. This equation is studied in a bounded domain without symmetry assumptions. It is assumed that the mean curvature of the boundary has a nondegenerate critical point. It is shown that there exists a spike-like stationary solution whose global maximum lies on the boundary. The derivation is based on Lyapunov-Schmidt reduction and the Brouwer fixed-point theorem.
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phase transition
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mean curvature of the boundary
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spike-like stationary solution
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Lyapunov-Schmidt reduction
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