Spiraling asymptotic profiles of competition-diffusion systems
Analysis of PDEs
2019-11-01 v2
Abstract
This paper describes the structure of the nodal set of segregation profiles arising in the singular limit of planar, stationary, reaction-diffusion systems with strongly competitive interactions of Lotka-Volterra type, when the matrix of the inter-specific competition coefficients is asymmetric and the competition parameter tends to infinity. Unlike the symmetric case, when it is known that the nodal set consists in a locally finite collection of curves meeting with equal angles at a locally finite number of singular points, the asymmetric case shows the emergence of spiraling nodal curves, still meeting at locally isolated points with finite vanishing order.
Keywords
Cite
@article{arxiv.1707.01051,
title = {Spiraling asymptotic profiles of competition-diffusion systems},
author = {Susanna Terracini and Gianmaria Verzini and Alessandro Zilio},
journal= {arXiv preprint arXiv:1707.01051},
year = {2019}
}