The 71st Midwest Partial Differential Equations Seminar May 11-12, 2013 Room TBA East Hall University of Michigan Ann Arbor, MI   Abstract Detail   Title: Quasi-static evolution and congested crowd motion We consider the relationship between Hele-Shaw evolution with drift, the porous medium equation with drift, and a congested crowd motion model. We first use viscosity solutions to show that the porous medium equation solutions converge to the Hele-Shaw solution as $m o infty$ provided the drift potential is strictly subharmonic. Next, using of the gradient flow structure of both the porous medium equation and the crowd motion model, we prove that the porous medium equation solutions also converge to the congested crowd motion as $m oinfty$. Combining these results lets us deduce that in the case where the initial data to the crowd motion model is given by a patch, or characteristic function, the solution evolves as a patch that is the unique solution to the Hele-Shaw problem. This is a joint work with Damon Alexander and Inwon Kim. Yao Yao University of Wisconsin Madison Email:  yaoyao@math.wisc.edu Phone: (310) 990-5580   BACK to Speaker Listing BACK to Conference Home   Sponsors National Science Foundation, Department of Mathematics at the University of Michigan