Seminars & Colloquia Calendar
The porous medium equation and concavity
Ben Weinkove (Nortwestern University)
Date & time: Tuesday, 09 November 2021 at 2:50PM - 3:50PM
Abstract: The porous medium equation is a nonlinear equation used to model gas diffusing in a porous medium. It is a degenerate parabolic flow with an evolving free boundary. In this talk I will discuss some examples which show that concavity of the gas pressure is not in general preserved along the flow. This answers an open problem of Vazquez. By work of Daskalopoulos-Hamilton-Lee, our results are sharp. This is joint work with Albert Chau.