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A variational problem for the spatial segregation of reaction-diffusion systems. (English) Zbl 1132.35397
Summary: 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.

MSC:
35K57 Reaction-diffusion equations
35J60 Nonlinear elliptic equations
35R35 Free boundary problems for PDEs
47J30 Variational methods involving nonlinear operators
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
92D25 Population dynamics (general)
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