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Spikey Steady States of a Class of Chemotaxis Mod

活動信息

  • 開始時間:2024-04-11 15:00:00
  • 活動地點:數(shù)學院114
  • 主講人:王學鋒

活動簡介

Chemotaxis is the directed movement of cells in response to the concentration gradient of chemical substances in their environment. Since the seminal work of Keller and Segel in 1970, where they first wrote down what now are called Keller-Segel models, there has been an intensive interest and large amount of work on these models, especially in the last 20 years. The most important phenomenon concerning chemotaxis is cell aggregation. To model this phenomenon mathematically, three methods have been developed. The first one, first proposed by Nanjundia and advanced by Childress and Percus formally, is to show the solution of the model blows up in finite time to form delta-singularity at several spots(pores) in the cell habitat; the second one, as pioneered by Lin, Ni and Takagi, is to use variational method (and Lyapunov-Schmidt method) to show the model has spikey steady states; the third one is to use the speaker’s method of combining Global Bifurcation Theorem and Helly’s compactness theorem to show the existence of spikey and transition layer solutions. Until now, the third method has been successful in dealing with some chemotaxis systems only in 1D or radially symmetric domains. The difficulty stems from proving the monotonicity of the second Neumann-Laplace eig

主講人介紹

王學鋒教授于2019年8月加入香港中文大學(深圳)。在此之前,他在杜蘭大學工作了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(lǐng)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(xiàn)新的數(shù)學現(xiàn)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(xiàn)的日益復雜的PDE模型提供通用的、易操作的工具。