On the existence of nonnegative continuous solutions of the Cahn-Hilliard equation (Q1188242)
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scientific article; zbMATH DE number 40268
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of nonnegative continuous solutions of the Cahn-Hilliard equation |
scientific article; zbMATH DE number 40268 |
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On the existence of nonnegative continuous solutions of the Cahn-Hilliard equation (English)
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13 August 1992
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The author investigates the Cahn-Hilliard equation in one space dimension for the case when the mobility vanishes if the concentration attains one of the limiting values 0 or 1. In this case, the fourth-order Cahn- Hilliard equation degenerates. The author uses approximation techniques to show that, under suitable smoothness assumptions on the mobility, a (generalized) solution exists which attains its values in the physically meaningful range [0,1].
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phase transitions
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spinodal decomposition
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existence theory
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regularity
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degenerate fourth-order problems
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