Title: The porous medium equation and concavity
Speaker: Ben Weinkove
Speaker Info: Northwestern University
Brief Description:
Special Note:
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 results of Daskalopoulos-Hamilton-Lee, our results are sharp. This is joint work with Albert Chau.Date: Tuesday, October 26, 2021