This article is part of the series Degenerate and Singular Differential Operators with Applications to Boundary Value Problems.

Open Access Research Article

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

M Badii1 and JI Díaz2*

Author Affiliations

1 Dipartimento di Matematica G. Castelnuovo, Università degli Studi di Roma "La Sapienza", P.le A. Moro 2, 00185 Roma, Italy

2 Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias, 3, 28040 Madrid, Spain

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Boundary Value Problems 2010, 2010:147301  doi:10.1155/2010/147301


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2010/1/147301


Received:30 July 2010
Accepted:1 November 2010
Published:2 November 2010

© 2010 M. Badii and J. I. Díaz.

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.

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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