Coexistence and segregation for strongly competing species in special domains

Monica Conti, Veronica Felli
2008 Interfaces and free boundaries (Print)  
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Dirichlet boundary conditions. For a class of nonconvex domains composed of balls connected by 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
more » ... ion phenomena and optimal partition problems. †
doi:10.4171/ifb/185 fatcat:jzygufqssbgdjj2iote7i64m54