学术报告: Boundary layers arising from chemotaxis models

发布日期:2017/06/08 10:58:46 | 阅读次数:370

报告题目:  Boundary layers arising from chemotaxis models 
报告人:   王治安教授(香港理工大学)                
报告时间: 6月10号15:30-16:30
报告地点: 太白校区非线性科学研究中心学术报告厅(312)

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. In this talk, we first consider the dynamics of the transformed Keller-Segel system in a bounded interval with time-dependent Dirichlet boundary conditions.  By imposing some conditions on the boundary data, we show that boundary layer profiles are present as chemical diffusion tends to zero and large-time profile of solutions will be determined by the boundary data (i.e. boundary stabilization). We employ the refined (weighted) energy estimates with the ``effective viscous flux" technique to show the emergence of boundary layer profiles. For asymptotic dynamics of solutions, we develop a new idea by exploring the convexity of an entropy expansion to get the basic $L^1$-estimate, on which our results are built up by the method of energy estimates. Finally we gain the results for the original singular Keller-Segel system by reversing the Cole-Hopf transformation. Numerical simulations are performed to interpret our analytical results and their implications.


报告人简介:王治安教授2007年于加拿大阿尔伯塔大学取得数学博士学位,2007年8月-2009年8月在美国明尼苏达大学作博士后,2009年8月-2010年8月在美国范德堡大学作助理教授,2010年8月至今工作于香港理工大学数学系。王治安教授多年来从事非线性偏微分方程的数学理论研究,在SIAM, J. Math. Ana, SIAM, J. Appl. Math, M3AS, Nonlinearity,  J. Differential Equations等高水平学术期刊上发表学术论文40余篇。

 

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