Finite Speed of Propagation for the Thin-Film Equation in Spherical Geometry

We show that a doubly degenerate thin-film equation obtained in modeling the flows of viscous coatings on spherical surfaces has a finite speed of propagation for nonnegative strong solutions and, hence, there exists an interface or a free boundary separating the regions, where the solution u > 0 and u = 0. By using local entropy estimates, we also establish the upper bound for the rate of propagation of the interface.