Singular limit of an activator-inhibitor type model

Marie Henry; Marie Henry

doi:10.3934/nhm.2012.7.781

Networks and Heterogeneous Media

2012, Volume 7, Issue 4: 781-803. doi: 10.3934/nhm.2012.7.781

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Singular limit of an activator-inhibitor type model

Marie Henry ^{1
,}

1.
CMI, Université de Provence, 39 rue Frédéric Joliot-Curie 13453 Marseille cedex 13

Received: 01 January 2012 Revised: 01 November 2012
35K57, 35B25, 35B50.

We consider a reaction-diffusion system of activator-inhibitor type arising in the theory of phase transition. It appears in biological contexts such as pattern formation in population genetics. The purpose of this work is to prove the convergence of the solution of this system to the solution of a free boundary Problem involving a motion by mean curvature.

Keywords:

Citation: Marie Henry. Singular limit of an activator-inhibitor type model[J]. Networks and Heterogeneous Media, 2012, 7(4): 781-803. doi: 10.3934/nhm.2012.7.781

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Abstract

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