Boundary Value Problems
Volume 2010 (2010), Article ID 147301, 17 pages
doi:10.1155/2010/147301
Research Article

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

M. Badii1 and J. I. Díaz2

1Dipartimento di Matematica G. Castelnuovo, Università degli Studi di Roma “La Sapienza”, P.le A. Moro 2, 00185 Roma, Italy
2Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias, 3, 28040 Madrid, Spain

Received 30 July 2010; Accepted 1 November 2010

Academic Editor: Vicentiu Radulescu

Copyright © 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.