DG-MP-PDE Seminar: Fourth order diffusion with geometric link to second order diffusion

We describe a fourth order family generalizing the linear-mobility thin film equation on R^n. In joint work with R. McCann we derive formally sharp converence rates to self-similarity, using a link to Denzler-McCann's analysis of a second order diffusion. We then show (joint with Matthes, McCann, Savare) that a certain range of nonlinearity allows the obtaining of rigorous results for the fourth-order evolution in 1 dimension.