On the Allen-Cahn equation in the Grushin plane: a monotone entire solution that is not one-dimensional

Details On the Allen-Cahn equation in the Grushin plane: a monotone entire solution that is not one-dimensional On the Allen-Cahn equation in the Grushin plane: a monotone entire solution that is not one-dimensional

2008-06-25

arxiv.org/abs/0806.4139v1

Mathematics

Analysis of PDEs

21 pages

Scientific paper

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.

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