Regularity of Interfaces for an Inhomogeneous Filtration Equation
M. Guedda, Danielle Hilhorst, Sergey Shmarev · Advanced Nonlinear Studies · 2001
Abstract We study the regularity of the interfaces for solutions of the degenerate parabolic equation p(x)u t =(u m ) xx, m > 1. AS opposed to the classical Porous Medium Equation, the interfaces in this equation may propagate with infinite speed and disappear within a finite time. We establish conditions on the initial function u(x, 0) and the function p(x) sufficient to provide the local C 1 -regularity of the interfaces until the moment of their disappearance. The interface equation (Darcy's law) is derived.