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

Walker, Christoph; Laurençot, Philippe; Hillairet, Matthieu; Escher, Joachim (2012), Weak solutions to a thin film model with capillary effects and insoluble surfactant, Nonlinearity, 25, 9, p. 2423. http://dx.doi.org/10.1088/0951-7715/25/9/2423

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00627948/fr/
Date
2012
Journal name
Nonlinearity
Volume
25
Number
9
Publisher
IOP Science
Pages
2423
Publication identifier
Metadata
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Author(s)
Walker, Christoph
Institut für Angewandte Mathematik [IFAM]
Laurençot, Philippe

Hillairet, Matthieu
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Escher, Joachim
Institute for Applied Mathematics [IFAM]
Abstract (EN)
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 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 under natural assumptions on the surface tension coefficient.
Subjects / Keywords
fourth-order diffusion; degenerate parabolic equation; thin film