We study existence and long-time behaviour of strong solutions for the thin film equation using a priori estimates in a weighted Sobolev space. This equation can be classified as a doubly degenerate fourth-order parabolic and it models coating flow on the outer surface of a sphere. It is shown that the strong solution asymptotically decays to the flat profile.
Localization, Smoothness, and Convergence to Equilibrium for a Thin Film Equation
Finite speed of propagation for the thin film equation in spherical geometry
Invariant Manifolds for the Thin Film Equation
![QR code for arXiv:1709.10496 [math.AP]](http://oss.arxitics.com/images/favicon.svg)