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 【明理讲坛】数学中心“椭圆型偏微分方程与非线性泛函分析”系列讲座 发布时间：2020-08-03【告诉好友】　【关闭窗口】 会议主题：王学锋教授学术讲座 　　会议时间：2020/8/5 09:00-12:00 　　腾讯会议ID：237 267 948 　　报告人： 王学锋 教授 （香港中文大学（深圳）） 　　报告题目：Bulk-Surface Coupling: Derivation of Two Models 　　报告摘要：It is well-known that cell polarization and cell division are caused by protein reaction-diffusion in the cytoplasm and on the cell membrane, which are coupled due to protein cycling between them. To model these cellular phenomena, numerous bulk-surface models have been proposed, which, in the simplest form, consist of one diffusion equation for inactive protein the cytoplasm and another one for active protein on the thickless membrane, with a flux boundary condition coupling the proteins in the bulk and on the surface. A rigorous derivation of such models seems lacking, which motivates this work. We assume that the membrane has positive but small thickness $\delta$ and that the phospholipid molecules in the membrane are optimally aligned and we start with two full models each of which contains reaction-diffusion equations in the bulk and the membrane, respectively, with reasonable transmission conditions linking the two. Then in the limit of $\delta\rightarrow 0$, we obtain two effective models, with one having the same form as the simplest bulk-surface model mentioned above, the other being a single diffusion equation in the cytoplasm with a dynamical boundary condition. Our models satisfy mass conservation property, which has been a yardstick for the existing bulk-surface models. Our investigation reveals that the optimal alignment of phospholipid molecules and the tangential diffusion in the cell membrane result in the surface diffusion in bulk-surface models, and that a single diffusion equation with a dynamical boundary condition may serve as a simpler alternative model for bulk-surface coupling. This is a joint work with Jingyu Li and Linlin Su. 　　报告人简介：王学锋，香港中文大学（深圳）教授，博导。主要研究方向是偏微分方程及其应用。1984年、1986年先后于北京大学数学系获学士学位和硕士学位，1990年于美国明尼苏达大学数学学院获博士学位。先后在美国明尼苏达大学、美国犹他大学和香港浸会大学等做访问研究员或访问教授。他在杜兰大学工作了26年，2016-2019年任职于南方科技大学，2019年8月加入香港中文大学（深圳）。他主持美国国家科学基金项目多项，若干论文发表在《CPAM》、《Duke Math.J》、《ARMA》、《SIAM》、《TAMS》、《CMP》等国际重要数学杂志上，论文被引用共达1700多次，近三年来在国际学术会议上给了20多个特邀报告，现担任一些国际重要数学杂志的编委或副主编。 【关闭窗口】