We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows indefinitely, the system reaches a state of coexistence of all the species in spatial segregation. Furthermore, the limit configuration is a local minimizer for the associated free energy.
Conti, M., Felli, V. (2009). Minimal coexistence configurations for multispecies systems. NONLINEAR ANALYSIS, 71(7-8), 3163-3175 [10.1016/j.na.2009.01.225].
Minimal coexistence configurations for multispecies systems
FELLI, VERONICA
2009
Abstract
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows indefinitely, the system reaches a state of coexistence of all the species in spatial segregation. Furthermore, the limit configuration is a local minimizer for the associated free energy.
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