Open Access

On the Time Periodic Free Boundary Associated to Some Nonlinear Parabolic Equations

Boundary Value Problems20102010:147301

DOI: 10.1155/2010/147301

Received: 30 July 2010

Accepted: 1 November 2010

Published: 2 November 2010

Abstract

We give sufficient conditions, being also necessary in many cases, for the existence of a periodic free boundary generated as the boundary of the support of the periodic solution of a general class of nonlinear parabolic equations. We show some qualitative properties of this free boundary. In some cases it may have some vertical shape (linking the free boundaries of two stationary solutions), and, under the assumption of a strong absorption, it may have several periodic connected components.

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Authors’ Affiliations

(1)
Dipartimento di Matematica G. Castelnuovo, Università degli Studi di Roma "La Sapienza"
(2)
Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid

Copyright

© M. Badii and J. I. Díaz. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.