Singular limit of an activator-inhibitor type model

Marie Henry

doi:10.3934/nhm.2012.7.781

Article Contents

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: December 31, 2011

Revised: October 31, 2012

Published: November 2012

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Abstract

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.

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Mathematics Subject Classification: 35K57, 35B25, 35B50.

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