应兰州大学数学与统计学院李万同教授和孙建文副教授的邀请香港中文大学（深圳）王学锋教授于2020年8月30日至8月31日访问兰州大学,期间将举办专题学术报告。

报告题目：Bulk-Surface Coupling: Derivation of Two Model

时    间：8月31日下午15:00-16:00

地    点：腾讯会议 App，会议 ID：961 272 346

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， Linlin Su， Yantao Wang.

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报告人简介

王学锋教授于2019年8月加入香港中文大学（深圳）。在此之前，他在杜兰大学工作了26年，2016-2019年在南方科技大学任职。他一直从事教学工作，从大一微积分到博士生专题课程。王学锋教授的研究领域是偏微分方程（PDE）。他的一些研究课题旨在通过典范的例子在简洁的框架下发现新的数学现象，提供新的视角，展示新的方法。 其它的课题（例如大范围分支理论和Krein-Rutman理论）是为分析应用中出现的日益复杂的PDE模型提供通用的、易操作的工具。

甘肃省高校应用数学与复杂系统省级重点实验室

数学与统计学院

萃英学院

2020年8月30日