On the retention of the interfaces in some elliptic and parabolic nonlinear problems

Luis Alvarez; Jesús Ildefonso Díaz

doi:10.3934/dcds.2009.25.1

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2009, Volume 25, Issue 1: 1-17. Doi: 10.3934/dcds.2009.25.1

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On the retention of the interfaces in some elliptic and parabolic nonlinear problems

Luis Alvarez^1, and
Jesús Ildefonso Díaz^2,

1.
Departamento de Informática y Sistemas., Universidad de Las Palmas de Gran Canaria, Campus de Tafira, 35017 Las Palmas
2.
Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid

Received: May 31, 2007

Revised: May 31, 2008

Published: December 2008

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Abstract

We study some retention phenomena on the free boundaries associated to some elliptic and parabolic problems of reaction-diffusion type. This is the case, for instance, of the waiting time phenomenon for solutions of suitable parabolic equations. We find sufficient conditions in order to have a discrete version of the waiting time property (the so called nondiffusion of the support) for solutions of the associated family of elliptic equations and prove how to pass to the limit in order to get this property for the solutions of the parabolic equation.

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Mathematics Subject Classification: Primary: 35J60, 35J70, 35K55, 35K65.

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