Finite speed of propagation for the thin-film equation in the spherical geometry
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.
How to Cite
Taranets, R. M. “Finite Speed of Propagation for the Thin-Film Equation in the Spherical Geometry”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 6, June 2019, pp. 840-51, https://umj.imath.kiev.ua/index.php/umj/article/view/1479.