We analysed some qualitative properties of the limit configuration of the solutions of a reaction–diffusion system of four competing species as the competition rate tends to infinity. Large interaction induces the spatial segregation of the species and only two limit configurations are possible: either there is a point where four species concur, a 4-point, or there are two points where only three species concur. We characterized, for a given datum, the possible 4-point configuration by means of the solution of a Dirichlet problem for the Laplace equation.
Spatial segregation Competition–Diffusion system Pattern formation
Mathematics Subject Classification
35J65 35Bxx 92D25
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The authors thank professor Andrea Dall’Aglio for many fruitful discussions. The authors are also very grateful to the anonymous referees for their insightful comments and helpful suggestions.