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Double layered solutions to the extended Fisher-Kolmogorov P.D.E.

We construct double layered solutions to the extended Fisher-Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work is to provide for the extended Fisher-Kolmogorov equation, the first examples of two-dimensional minimal solutions, since these solutions play a crucial role in phase transition models, and are closely related to the De Giorgi conjecture.

preprint2020arXivOpen access
Panayotis Smyrnelis
math.AP
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Panayotis Smyrnelis

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