應yl7703永利官網李萬同教授和孫建文副教授的邀請香港中文大學（深圳）王學鋒教授于2020年8月30日至8月31日訪問蘭州大學,期間將舉辦專題學術報告。

報告題目：Bulk-Surface Coupling: Derivation of Two Model

時    間：8月31日下午15:00-16:00

地    點：騰訊會議 App，會議 ID：961 272 346

報告摘要：

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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報告人簡介

王學鋒教授于2019年8月加入香港中文大學（深圳）。在此之前，他在杜我校學工作了26年，2016-2019年在南方科技大學任職。他一直從事教學工作，從大一微積分到博士生專題課程。王學鋒教授的研究領域是偏微分方程（PDE）。他的一些研究課題旨在通過典范的例子在簡潔的框架下發(fā)現新的數學現象，提供新的視角，展示新的方法。 其它的課題（例如大范圍分支理論和Krein-Rutman理論）是為分析應用中出現的日益復雜的PDE模型提供通用的、易操作的工具。

甘肅省高校應用數學與復雜系統(tǒng)省級重點實驗室

yl7703永利官網

萃英學院

2020年8月30日