In this paper we study a class of stationary states for reaction-diffusion systems of k ≥ 3 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
Conti, M., Terracini, S., Verzini, G. (2005). A variational problem for the spatial segregation of reaction-diffusion systems. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 54(3), 779-815 [10.1512/iumj.2005.54.2506].
A variational problem for the spatial segregation of reaction-diffusion systems
TERRACINI, SUSANNA;
2005
Abstract
In this paper we study a class of stationary states for reaction-diffusion systems of k ≥ 3 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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