Boundary-layer problem for the Keller-Segel model with physical boundary conditions

報(bào)告題目：Boundary-layer problem for the Keller-Segel model with physical boundary conditions

報(bào) 告 人：王治安 教授 香港理工大學(xué)

邀請(qǐng)人：王裴昕

報(bào)告時(shí)間：2024年10月24日（周四） 10：00（北京時(shí)間）

報(bào)告地點(diǎn)： 騰訊會(huì)議：464-235-970 會(huì)議密碼：1024

https://meeting.tencent.com/dm/HMIX7SzPnT1v

報(bào)告人簡(jiǎn)介：王治安， 香港理工大學(xué)應(yīng)用數(shù)學(xué)系教授，華中師大本科碩士， 加拿大艾伯塔大學(xué)應(yīng)用數(shù)學(xué)博士，美國(guó)明尼蘇達(dá)大學(xué)應(yīng)用數(shù)學(xué)所博士后。主要從事與生物數(shù)學(xué)相關(guān)的偏微分方程建模及分析研究。目前已在Proc. London Math. Soc 、 J. London Math. Soc. 、 J. Math. Biol.、JMPA、CPDE、SIAM J. Math. Anal.、SIAM J. Appl. Math. 、Indiana U. Math. J. 等雜志上發(fā)表學(xué)術(shù)論文100多篇。現(xiàn)擔(dān)任雜志 J. Mathematical Biology, DCDS-B， MBE等雜志編委。曾獲香港數(shù)學(xué)會(huì)青年學(xué)者獎(jiǎng)。

報(bào)告摘要:In this talk, we shall discuss the boundary layer problem of the singular Keller-Segel model with physical boundary conditions in any dimensions. First, we obtain the existence and uniqueness of boundary-layer solution to the steady-state problem and identify the boundary-layer profile and thickness near the boundary. Then we find the asymptotic expansion of boundary-layer profile in terms of the radius for the radially symmetric domain, which can assert how the boundary curvature affects the boundary-layer thickness. Finally, we establish the nonlinear stability of the unique boundary-layer steady state solution with exponential convergence rate for the radially symmetric domain.

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院