报告题目：Spikey Steady States of a Class of Chemotaxis Models in Convex Symmetric Planar Domains
报 告 人：王学锋 教授 香港中文大学（深圳）
报告时间：2024年4月11日（星期四） 15:00-16:00
报告地点：数学科学学院114（小报告厅）
校内联系人：代国伟 教授 联系电话：84708351-8502
报告摘要：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 eigenfunction, and then proving that the monotonicity remains unchanged on the bifurcation branch. In the joint work with Dr. Hongze Wang, we are able to make a progress so that the third method works on some special 2D domains, including “ellipse-like” planar domains. The works on the “hot spots” conjecture (a 50-year-old open problem on the second Neumann-Laplace eigenfunction), in particular that of Hongbin Chen, Yi Li and Lihe Wang, play an important role in our proofs.
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。
