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）  

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 an enormous 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，香港中文大学（深圳）校长讲座教授、研究生院院长，曾任Tulane大学教授，南方科技大学特聘教授、千人计划专家，国际知名椭圆和抛物方程研究领域的专家，担任一些国际重要数学杂志的副主编或编委。  

报告时间：2024年9月27日（周五）上午9：30-10：30  

报告地点：教二楼727  

联系人：吴雅萍、许文兵