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Geometric Analysis Seminar

The porous medium equation and concavity

Ben Weinkove (Nortwestern University)

Location:  zoom
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.

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