On the Time Periodic Free Boundary Associated to Some Nonlinear Parabolic Equations
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
Boundary Value Problems 2010, 2010:147301 doi:10.1155/2010/147301Published: 2 November 2010
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.