Infinitely many saturated travelling waves for a degenerate Fisher-KPP equation not in divergence form

Fuente: arXiv
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Main Authors: Alfaro, Matthieu, Herda, Maxime, Natale, Andrea
Format: Preprint
Published: 2025
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author Alfaro, Matthieu
Herda, Maxime
Natale, Andrea
author_facet Alfaro, Matthieu
Herda, Maxime
Natale, Andrea
contents We consider an epidemic model with distributed-contacts. When the contact kernel concentrates, one formally reaches a very degenerate Fisher-KPP equation with a diffusion term that is not in divergence form. We make an exhaustive study of its travelling waves. For every admissible speed, there exist not only a unique non-saturated (smooth) wave but also infinitely many saturated (sharp) ones. Furthermore their tails may differ from what is usually expected. These results are thus in sharp contrast with their counterparts on related models.
format Preprint
id arxiv_https___arxiv_org_abs_2502_11589
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Infinitely many saturated travelling waves for a degenerate Fisher-KPP equation not in divergence form
Alfaro, Matthieu
Herda, Maxime
Natale, Andrea
Analysis of PDEs
35K65, 35C07, 92D30
We consider an epidemic model with distributed-contacts. When the contact kernel concentrates, one formally reaches a very degenerate Fisher-KPP equation with a diffusion term that is not in divergence form. We make an exhaustive study of its travelling waves. For every admissible speed, there exist not only a unique non-saturated (smooth) wave but also infinitely many saturated (sharp) ones. Furthermore their tails may differ from what is usually expected. These results are thus in sharp contrast with their counterparts on related models.
title Infinitely many saturated travelling waves for a degenerate Fisher-KPP equation not in divergence form
topic Analysis of PDEs
35K65, 35C07, 92D30
url https://arxiv.org/abs/2502.11589