PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Xiantao Li, Stephanie Zerby, Chun Liu, Fei Wang.

Title:Long time behavior of solutions to the 2D Keller-Segel equation with degenerate diffusion
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Yao Yao, Georgia Tech
Abstract:
The Keller-Segel equation is a nonlocal PDE modeling the collective motion of cells attracted by a self-emitted chemical substance. When this equation is set up in 2D with a degenerate diffusion term, it is known that solutions exist globally in time, but their long-time behavior remains unclear. In a joint work with J.Carrillo, S.Hittmeir and B.Volzone, we prove that all stationary solutions must be radially symmetric up to a translation, and use this to show convergence towards the stationary solution as the time goes to infinity. I will also discuss another joint work with K.Craig and I.Kim, where we let the power of degenerate diffusion go to infinity in the 2D Keller-Segel equation, so it becomes an aggregation equation with a constraint on the maximum density. We will show that if the initial data is a characteristic function, the solution will converge to the characteristic function of a disk as the time goes to infinity with certain convergence rate.

Room Reservation Information

Room Number:MB106
Date:04 / 11 / 2016
Time:02:30pm - 03:30pm