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

Joachim Escher (1) , Matthieu Hillairet (2) , Philippe Laurencot (3) , Christoph Walker (4)

1 IFAM - Institute for Applied Mathematics
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 IFAM - Institut für Angewandte Mathematik

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.

Mots clés: thin film; degenerate parabolic equation; fourth-order diffusion

Domaines: Equations aux dérivées partielles [math.AP]

Joachim Escher, Matthieu Hillairet, Philippe Laurencot, Christoph Walker. Weak solutions to a thin film model with capillary effects and insoluble surfactant. Nonlinearity, 2012, 25, pp.2423--2441. ⟨10.1088/0951-7715/25/9/2423⟩. ⟨hal-00627948⟩