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# Inwon Kim : Quasi-static evolution and congested crowd motion

In this talk we investigate the relationship between Hele-Shaw evolution with a drift and a transport equation with a drift potential, where the density is transported with a constraint on its maximum. The latter model, in a simplified setting, describes the congested crowd motion with a density constraint. When the drift potential is convex, the crowd density is likely to aggregate, and thus if the initial density starts as a patch (i.e. if it is a characteristic function of some set) then it is expected that the density evolves as a patch. We show that the evolving patch satisfies a Hele-Shaw type equation. This is joint work with Damon Alexander and Yao Yao.

**Category**: Applied Math and Analysis**Duration**: 01:34:55**Date**: April 22, 2013 at 4:25 PM**Views**: 122-
**Tags:**seminar, Applied Math And Analysis Seminar

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