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

Roman Taranets

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arXiv · 1802.02031

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

Roman Taranets

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Abstract

We show that a double degenerate thin film equation, which originated from modeling of viscous coating flow on a spherical surface, has finite speed of propagation for nonnegative strong solutions and hence there exists an interface or free boundary separating the regions where solution $u>0$ and $u=0$. Using local entropy estimates we also obtain an upper bound for the rate of the interface propagation.

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Roman Taranets. 2018-02-06. Finite speed of propagation for the thin film equation in spherical geometry. https://arxiv.org/abs/1802.02031

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