Coexistence and Segregation for Strongly Competing Species in Special Domains

Details Coexistence and Segregation for Strongly Competing Species in Special Domains Coexistence and Segregation for Strongly Competing Species in Special Domains

2006-02-15

arxiv.org/abs/math/0602334v3

Mathematics

Analysis of PDEs

Scientific paper

We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Dirichlet boundary conditions. For a class of nonconvex domains composed by balls connected with thin corridors, we show the occurrence of pattern formation (coexistence and spatial segregation of all the species), as the competition grows indefinitely. As a result we prove the existence and uniqueness of solutions for a remarkable system of differential inequalities involved in segregation phenomena and optimal partition problems.

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