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

  • R. M. Taranets

Abstract

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.
Published
25.06.2019
How to Cite
TaranetsR. 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, http://umj.imath.kiev.ua/index.php/umj/article/view/1479.
Section
Research articles