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Strong Solutions of the Thin Film Equation in Spherical Geometry

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Modern Mathematics and Mechanics

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

We study existence and long-time behaviour of strong solutions for the thin film equation using a priori estimates in a weighted Sobolev space. This equation can be classified as a doubly degenerate fourth-order parabolic and it models coating flow on the outer surface of a sphere. It is shown that the strong solution asymptotically decays to the flat profile.

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Acknowledgements

This paper is supported by Ministry of Education and Science of Ukraine, grant number is 0118U003138.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of the NASU, Sloviansk, Ukraine

    Roman M. Taranets

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  1. Roman M. Taranets
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Editors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

  2. National Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    Michael Z. Zgurovsky

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Taranets, R.M. (2019). Strong Solutions of the Thin Film Equation in Spherical Geometry. In: Sadovnichiy, V., Zgurovsky, M. (eds) Modern Mathematics and Mechanics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-96755-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-96755-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96754-7

  • Online ISBN: 978-3-319-96755-4

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