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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Yao Yao
Georgia Tech
Title: Long time behavior of solutions to the 2D Keller-Segel equation with degenerate diffusion

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.

Recording: http://mm.math.cmu.edu/recordings/cna/YaoYao_small.mp4
Date: Tuesday, September 27, 2016
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Slepcev