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Research Article | Open Access

Spatial segregation limit of traveling wave solutions for a fully nonlinear strongly coupled competitive system

Léo Girardin1( ), Danielle Hilhorst2
Institut Camille Jordan, Université Claude Bernard Lyon-1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d'Orsay, 91405 Orsay Cedex, France
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Abstract

The paper is concerned with a singular limit for the bistable traveling wave problem in a very large class of two-species fully nonlinear parabolic systems with competitive reaction terms. Assuming existence of traveling waves and enough compactness, we derive and characterize the limiting problem. The assumptions and results are discussed in detail. The free boundary problem obtained at the limit is specified for important applications.

Keywords

Lotka–Volterratraveling wavebistabilitynonlinear diffusionnonlinear advection

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Electronic Research Archive
Volume 30 Issue 5,
May 2022
Pages 1748-1773
DOI: 10.3934/era.2022088

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Cite this article:
Girardin L, Hilhorst D. Spatial segregation limit of traveling wave solutions for a fully nonlinear strongly coupled competitive system. Electronic Research Archive, 2022, 30(5): 1748-1773. https://doi.org/10.3934/era.2022088

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Received: 10 September 2021
Revised: 14 December 2021
Accepted: 22 December 2021
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)