A free boundary problem for a parabolic system describing an ecological model

Abstract

In this paper, the one-dimensional quasilinear Verigin problem and the relative diffraction problem are Studied. This free boundary problem describes a motion of the interface between two groups of animals. The existence and uniqueness of a classical solution locally in time are obtained. The continuous dependence of the solution on the internal boundary and the smoothness of the free boundary are also given. (C) 2007 Elsevier Ltd. All rights reserved.