Finite speed of propagation for the thin film equation in spherical geometry

Abstract

We show that a double degenerate thin film equation, which originated from modeling of viscous coating flow on a spherical surface, has finite speed of propagation for nonnegative strong solutions and hence there exists an interface or free boundary separating the regions where solution $u>0$ and $u=0$. Using local entropy estimates we also obtain an upper bound for the rate of the interface propagation.