On the limit configuration of four species strongly competing systems

  • Flavia LanzaraEmail author
  • Eugenio Montefusco


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 



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.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica G. CastelnuovoSapienza Università di RomaRomeItaly

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