Solutions of the Allen-Cahn equation which are invariant under screw-motion (Q431146)
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scientific article; zbMATH DE number 6050520
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solutions of the Allen-Cahn equation which are invariant under screw-motion |
scientific article; zbMATH DE number 6050520 |
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Solutions of the Allen-Cahn equation which are invariant under screw-motion (English)
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26 June 2012
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The paper deals with the Allen-Cahn equation \[ \Delta u-F'(u)=0, \] where \(F(u)\) is a double wall potential. Entire solutions are studied which are defined in the \(3\)-dimensional Euclidean space and which are invariant under screw-motion. In particular, the authors discuss existence and non existence of nontrivial solutions whose nodal set is a helicoid of \({\mathbb R}^{3}.\)
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Allen-Cahn equation
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entire solutions
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