A variational problem for the spatial segregation of reaction--diffusion systems

Details A variational problem for the spatial segregation of reaction--diffusion systems A variational problem for the spatial segregation of reaction--diffusion systems

2003-12-10

arxiv.org/abs/math/0312210v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

In this paper we study a class of stationary states for reaction--diffusion systems of $k\geq 3$ 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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