The "Linear" Limit of Thin Film Flows as an Obstacle-Type Free Boundary Problem

We study the limit as n 0 of the nonnegative, self-similar source-type solutions of the thin film equation ut + (unuxxx)x = 0. We obtain a unique limiting function u, which is a solution of an obstacle-type free boundary problem, with the constraint u 0, associated with the linear equation ut + uxxxx = 0. The function u is C1 for t > 0 and has finite speed of propagation, the positivity set {u > 0} being bounded by two contact lines x =

• Type: Journal
• Year: 2000
• Where: SIAMAM
• Authors: Fernando Quirós, Francisco Bernis, Josephus Hulshof
• Keywords: Free Boundary Problem, Linear Equation, SIAMAM 2000, Source-type Solutions