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Weak solutions to a thin film model with capillary effects and insoluble surfactant

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Published 2 August 2012 • © 2012 IOP Publishing Ltd & London Mathematical Society
, , Citation Joachim Escher et al 2012 Nonlinearity 25 2423 DOI 10.1088/0951-7715/25/9/2423

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Author e-mails

escher@ifam.uni-hannover.de

hillairet@ceremade.dauphine.fr

laurenco@math.univ-toulouse.fr

walker@ifam.uni-hannover.de

Author affiliations

1 Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, D–30167 Hannover, Germany

2 CEREMADE, UMR CNRS 7534, Université de Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, F–75775 Paris Cedex 16, France

3 Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, F–31062 Toulouse Cedex 9, France

Dates

  1. Received 28 September 2011
  2. Published

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0951-7715/25/9/2423

Abstract

The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the film height is a degenerate parabolic of fourth order and coupled to a second order parabolic equation for the surfactant concentration. It is shown that nonnegative weak solutions exist.

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10.1088/0951-7715/25/9/2423