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

Authors

  • 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.

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Published

25.06.2019

Issue

Section

Research articles

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.