报告摘要：
| The original well-known Keller-Segel system describing the chemotactic wave propagation remains poorly understood in many aspects due to the logarithmic singularity. As the chemical assumption rate is linear, the singular Keller-Segel model can be converted, via a Cole-Hopf type transformation, into a system of viscous conservation laws without singularity. But the chemical diffusion rate parameter for the original Keller-Segel system now plays a dual role in the transformed system by acting as the coefficients of both diffusion and nonlinear convection terms. This is a new feature and raises challenges in deriving the uniform estimates in chemical diffusion. In this talk, we first consider the dynamics of the transformed Keller-Segel system in a bounded interval. By imposing appropriate boundary conditions, we show that boundary layer profiles are present as chemical diffusion tends to zero. Furthermore we identify the structure of boundary layers and prove its stability. Finally we interpret the results for the original singular Keller-Segel.
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