Strong Solutions of the Thin Film Equation in Spherical Geometry

  • Roman M. Taranets
Part of the Understanding Complex Systems book series (UCS)


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.


Thin film Equation Strong Solution Weighted Sobolev Spaces Flat Profile Long-time Behavior 
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This paper is supported by Ministry of Education and Science of Ukraine, grant number is 0118U003138.


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Roman M. Taranets
    • 1
  1. 1.Institute of Applied Mathematics and Mechanics of the NASUSlovianskUkraine

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