Center for Nonlinear Analysis
CNA Home
People
Seminars
Publications
Workshops and Conferences
CNA Working Groups
CNA Comments Form
Summer Schools
Summer Undergraduate Institute
PIRE
Cooperation
Graduate Topics Courses
SIAM Chapter Seminar
Positions
Contact |
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.aviRecording (mp4): http://mm.math.cmu.edu/recordings/cna/CNA-YaoYaoTape-Oct-03-2013.mp4Date: Thursday, October 3, 2013Time: 1:30 pmLocation: Wean Hall 7218Submitted by: David Kinderlehrer |