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 are stable and they satisfy a good energy estimate. However, they are not necessarily one-dimensional, as a counter-example shows.
ON THE ALLEN-CAHN EQUATION IN THE GRUSHIN PLANE: A MONOTONE ENTIRE SOLUTION THAT IS NOT ONE-DIMENSIONAL / Birindelli, Isabella; Enrico, Valdinoci. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 29:3(2011), pp. 823-838. [10.3934/dcds.2011.29.823]
ON THE ALLEN-CAHN EQUATION IN THE GRUSHIN PLANE: A MONOTONE ENTIRE SOLUTION THAT IS NOT ONE-DIMENSIONAL
BIRINDELLI, Isabella;
2011
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 are stable and they satisfy a good energy estimate. However, they are not necessarily one-dimensional, as a counter-example shows.File allegati a questo prodotto
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