Nonlinear 4th order diffusion equations by optimal transport

PDE Seminar
Tuesday, May 5, 2009 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 255
Giuseppe Savare РUniversità degli Studi di Pavia, Italy
Michael Westdickenberg
Some interesting nonlinear fourth-order parabolic equations, including the "thin-film" equation with linear mobility and the quantum drift-diffusion equation, can be seen as gradient flows of first-order integral functionals in the Wasserstein space of probability measures. We will present some general tools of the metric-variational approach to gradient flows which are useful to study this kind of equations and their asymptotic behavior. (Joint works in collaboration with U.Gianazza, R.J. McCann, D. Matthes, G. Toscani)