English

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

Analysis of PDEs 2020-05-28 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2005.13427,
  title  = {Double layered solutions to the extended Fisher-Kolmogorov P.D.E.},
  author = {Panayotis Smyrnelis},
  journal= {arXiv preprint arXiv:2005.13427},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:1903.09473