Spiraling asymptotic profiles of competition-diffusion systems

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.

References in corpus (1)

• Uniform bounds for strongly competing systems: the optimal Lipschitz case

Cited by in corpus (3)

• A spiral interface with positive Alt-Caffarelli-Friedman limit at the origin
• On the limit configuration of four species strongly competing systems
• Rotating Spirals in segregated reaction-diffusion systems