Two generalisations of the thin film equation

Authors:
J. R. King
Affiliations:
Division of Theoretical Mechanics University of Nottingham, Nottingham NG7 2RD, U.K.
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2001

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Abstract

This paper is concerned with two generalisations of the widely studied thin film equation u"t = -(u^nu"x"x"x)"x. Both are degenerate fourth-order parabolic equations in conservation form; the first is which shares the scaling properties of the thin film equation (with special cases arising in applications and in earlier analyses), while the second is a doubly nonlinear equation which is relevant to capillary driven flows of thin films of power-law fluids. We focus on giving a characterisation of nonnegative mass preserving compactly supported solutions, exploiting local analyses about the edge of the support and special closed form solutions; however, other properties are also noted and open questions raised.