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

2003/12/10 by Monica Conti, Susanna Terracini, Conti, Monica +3 · 5 citations
Mathematics · #35J65 #58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:35J65 #msc:58E05

paper · pdf · doi:10.48550/arxiv.math/0312210

32 pages

arxiv created 2003/12/10 · arxiv updated 2009/12/01

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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• A survey on the optimal partition problem
• Gamma Convergence of Partially Segregated Elliptic Systems
• Spectral minimal partitions of unbounded domains
• A nonlinear model for long-range segregation
• The Gross-Pitaewskii equation with time and space dependent coefficients

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