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# Yao Yao : Long time behavior of solutions to the 2D Keller-Segel equation with degenerate diffusion

In this talk I will discuss the Keller-Segel equation, which 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 remain unclear. To answer this question, we investigate a general aggregation equation with degenerate diffusion, and prove that all stationary solutions must be radially symmetric up to a translation. As a consequence, this enables us to obtain a convergence result for solutions to 2D Keller-Segel equation with degenerate diffusion as the time goes to infinity. This is a joint work with J. Carrillo, S. Hittmeir and B. Volzone.

**Category**: Applied Math and Analysis**Duration**: 01:34:50**Date**: October 5, 2015 at 4:25 PM**Views**: 112-
**Tags:**seminar, Applied Math And Analysis Seminar

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