Finite speed of propagation for the thin-film equation in the spherical geometry - Taranets, R. M. (Ukrains’kyi Matematychnyi Zhurnal, 2019)
UDC 517.953 We show that a double degenerate thin-film equation obtained in modeling of a flow of viscous coating on the spherical surface 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 $u=0.$ Using local entropy estimates, we also obtain the upper bound for the rate of the interface propagation.