学术报告（江杰 11.09）

摘要：

We would like to report our recent research on a Keller-Segel model with signal-dependent motilities. This model was originally proposed by Keller and Segel in their seminal work in 1971, which models the cellular movements due to a local sensing chemotaxis. The model features a signal-dependent motility which may vanish as the concentration becomes unbounded. Thus degeneracy is the main obstacle in analysis. In our work, we develop a new comparison method based on the nonlinear structure which provides us an explicit point-wise upper bound estimate for the concentration. Then, we study the global existence of classical solutions and discuss their boundedness and asymptotic behavior. Moreover, a critical mass phenomenon as well as an infinite-time blowup was verified in the two-dimensional setting.

The talk is based on my recent joint work with K. Fujie from Tohoku University.