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Qianqian Hou-Boundary Layer Problems in Chemotaxis Models
发布人:赖旭东  发布时间:2018-04-17   浏览次数:10

Title: Boundary Layer Problems in Chemotaxis Models

Qianqian Hou The Hong Kong Polytechnic University

Abstract:  This talk is concerned with the zero-diffusion limit of a viscous  hyperbolic system transformed via a Cole-Hopf transformation from a  singular chemotactic system modeling the initiation of tumor  angiogenesis. It was previously found by Li and Zhao (2015) that when  prescribed with Dirichlet boundary conditions, the system possesses  boundary layers at the boundaries in an bounded interval $(0,1)$ as the  chemical diffusion rate (denoted by $\va>0$) is small, however the  rigorously mathematical justification is left open. In this talk, we  fist rigorously justify the existence of boundary layers (BLs), where  outside the BLs the solution with $\va>0$ converges to the one with  $\va=0$, but inside the BLs the convergence no longer holds.  We then  proceed to prove the stability of boundary layer solutions and identify  the precise structure of boundary layer solutions. Roughly speaking, we  justify that the solution with $\va>0$ converges to the solution with  $\va=0$ (outer layer) plus the (inner) boundary layer solutions with  the optimal rate at order of $O(\va^{1/2})$, where the outer and inner  layer solutions are well determined by explicit equations. Finally, we  covert the result for the transformed system to the original  pre-transformed chemotaxis system and discuss the biological  implications of our results.

Time and Place: 16:00-17:00, April 19, 2018,Gewubuilding, Room 522