|Date: Friday, January 16, 2015
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: The moving contact line in viscous thin films: a singular free boundary problem
Abstract: We are interested in the thin-film equation with quadratic mobility and zero contact angle, modeling the height of a viscous thin-film with a linear Navier-slip condition at the liquid-solid interface. This degenerate-parabolic fourth-order problem has the contact line (the triple junction between the three phases liquid, gas, and solid) as a free boundary. Starting with the analysis of source-type self-similar solutions, we conclude that solutions cannot be expected to be smooth and explicitly characterize the singular expansion of such solutions at the free boundary. With this understanding, we are able to prove a well-posedness result of the corresponding full parabolic problem. We conclude the talk with an overview of other questions and results, such as the generalization to thin-film equations with general mobility, higher regularity, the convergence to the source-type self-similar solution, or asymptotics related to Tanner's law. Many of the presented results are joint with Lorenzo Giacomelli, Hans Knüpfer, and Felix Otto.
Speaker: Manuel Gnann
Institution: Fields Institute and the University of Michigan
Event Organizer: Selim Esedoglu email@example.com