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Ukrainian Mathematical Journal

, Volume 71, Issue 6, pp 956–969 | Cite as

Finite Speed of Propagation for the Thin-Film Equation in Spherical Geometry

  • R. M. TaranetsEmail author
Article

We show that a doubly degenerate thin-film equation obtained in modeling the flows of viscous coatings on spherical surfaces 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. By using local entropy estimates, we also establish the upper bound for the rate of propagation of the interface.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesSlovianskUkraine

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