Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On the Time Periodic Free Boundary Associated to Some Nonlinear Parabolic Equations | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 147301 17 pages doi 2010 147301 Research Article On the Time Periodic Free Boundary Associated to Some Nonlinear Parabolic Equations M. Badii1 and J. I. Diaz2 1 Dipartimento di Matematica G. Castelnuovo Universita degli Studi di Roma La Sapienza A. Moro 2 00185 Roma Italy 2 Departamento de Matemdtica Aplicada Facultad de Matemdticas Universidad Complutense de Madrid Plaza de las Ciencias 3 28040 Madrid Spain Correspondence should be addressed to J. I. Diaz Received 30 July 2010 Accepted 1 November 2010 Academic Editor Vicentiu Radulescu Copyright 2010 M. Badii and J. I. Diaz. 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. 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. 1. Introduction This paper deals with several qualitative properties of the time periodic free boundary generated by the solution of a general class of second-order quasilinear equations. To simplify the exposition we will fix our attention in the problem formulated on the following terms ut - àpu 1f ù g in Q Q X R u x f h x f on s dQ X R P u x f T u x f in Q. Here T 0 Q c RNN 1 denotes an open bounded and regular set Apu div Vu p-2Vu p 1 is the so-called p-Laplacian operator 1 is a positive parameter and 2 Boundary Value Problems the data f g and h are assumed to satisfy the following .
