The Thin Film Equation with Non-Zero Contact Angle: A Singular Perturbation Approach

In this paper we consider the thin film equation with prescribed non-zero contact angle condition for a large class of mobility coefficients, in dimension 1. We prove the global in time existence of weak solutions by using a diffuse approximation of the free boundary condition. This approach, which can be physically motivated by the introduction of singular disjoining/conjoining pressure forces had been suggested in particular by Bertsch et al. in 11 Bertsch , M. , Giacomelli , L. , Karali , G. ( 2005 ). Thin-film equations with “partial wetting” energy: Existence of weak solutions . Phys. D 209 : 17 – 27 .Crossref], Web of Science ®] , Google Scholar]].