On the allen-cahn equation in the grushin plane: A monotone entire solution that is not one-dimensional

Isabeau Birindelli; Enrico Valdinoci

doi:10.3934/dcds.2011.29.823

On the allen-cahn equation in the grushin plane: A monotone entire solution that is not one-dimensional

Isabeau Birindelli, Enrico Valdinoci

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider solutions of the Allen-Cahn equation in the whole Grushin plane and we show that if they are monotone in the vertical direction, then they are stable and they satisfy a good energy estimate. However, they are not necessarily one-dimensional, as a counter-example shows.

Original language	English
Pages (from-to)	823-838
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems
Volume	29
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2011.29.823
Publication status	Published - 1 Mar 2011
Externally published	Yes

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10.3934/dcds.2011.29.823

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title = "On the allen-cahn equation in the grushin plane: A monotone entire solution that is not one-dimensional",

abstract = "We consider solutions of the Allen-Cahn equation in the whole Grushin plane and we show that if they are monotone in the vertical direction, then they are stable and they satisfy a good energy estimate. However, they are not necessarily one-dimensional, as a counter-example shows.",

keywords = "Allen-Cahn equation, Grushin plane, Symmetry problmes",

author = "Isabeau Birindelli and Enrico Valdinoci",

year = "2011",

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KW - Symmetry problmes

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On the allen-cahn equation in the grushin plane: A monotone entire solution that is not one-dimensional

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