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arXiv · 1707.01051

Spiraling asymptotic profiles of competition-diffusion systems

Susanna Terracini·Gianmaria Verzini·Alessandro Zilio
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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.

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Susanna Terracini, Gianmaria Verzini, Alessandro Zilio. 2019-10-30. Spiraling asymptotic profiles of competition-diffusion systems. https://doi.org/10.1002/cpa.21823

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