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CNA Seminar
Yao Yao
University of Wisconsin
Title: Quasi-static evolution and congested crowd motion

Abstract: In this talk we investigate a transport equation with a drift potential, where a constraint on the L^\infty norm is imposed on the density. This 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 the density evolves like a patch. We show that patch evolves according to a quasi-static evolution equation, which is a free boundary problem and has some connection with the Hele-Shaw equation. To show this result we make use of both viscosity solutions theory as well as the gradient flow structure of the problem. This is a joint work with Damon Alexander and Inwon Kim.

Recording (avi): http://mm.math.cmu.edu/recordings/cna/CNA-YaoYaoTape-Oct-03-2013.avi
Recording (mp4): http://mm.math.cmu.edu/recordings/cna/CNA-YaoYaoTape-Oct-03-2013.mp4
Date: Thursday, October 3, 2013
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer