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In this paper we study a class of stationary states reaction-diffusion systems of three or more densities having disjoint supports. For a class of segregation states governed by a variational principle we prove existence and provide conditions for uniqueness. Some qualitative properties and the local regularity both of the densities and of their free boundaries are established in the more general context of a functional class characterized by differential inequalities.
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Conti et al. (2005) studied this question.
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