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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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 6, pp. 840–851, June, 2019.
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Taranets, R.M. Finite Speed of Propagation for the Thin-Film Equation in Spherical Geometry. Ukr Math J 71, 956–969 (2019). https://doi.org/10.1007/s11253-019-01690-z
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DOI: https://doi.org/10.1007/s11253-019-01690-z