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Article Dans Une Revue Communications on Pure and Applied Mathematics Année : 2019

Spiraling Asymptotic Profiles of Competition‐Diffusion Systems

Résumé

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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Dates et versions

hal-02340932 , version 1 (31-10-2019)

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Susanna Terracini, Gianmaria Verzini, Alessandro Zilio. Spiraling Asymptotic Profiles of Competition‐Diffusion Systems. Communications on Pure and Applied Mathematics, 2019, 72 (12), pp.2578-2620. ⟨10.1002/cpa.21823⟩. ⟨hal-02340932⟩
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