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Dynamics of spike in a Keller-Segel’s minimal chemotaxis model - Prof. Xinfu Chen (University of Pittsburgh, USA)

作者:   来源:  时间:2018-06-08

题目:Dynamics of spike in a Keller-Segel’s minimal chemotaxis model

报告人: Prof. Xinfu Chen (University of Pittsburgh, USA)

Abstract:

The dynamics are studied for the Keller-Segel’s minimal chemotaxis model  

          

on a bounded interval with homogeneous Neumann boundary conditions, where  and k>>1 are parameters and the total mass of u is scaled to be one. In general, the dynamics can be divided into three stages; the first stage is very short in which u quickly becomes a delta like function with mass concentrated near the point of global maximum of v; in the second stage, the point of the global maximum of v drifts towards the boundary of the domain and reaches it at the end of the second stage; in the third stage, the profile of the solution evolves to a steady state profile. This paper considers a special case in which the relaxation parameter τ is set to be zero, so the first stage takes no time. A free boundary problem describing the second stage is presented. Rigorous asymptotic behavior is proven for the third stage evolution.

时间:6月8日(周五) 15:30-16:30

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