一、报告题目：The Existence of Moving Spike Patterns in an Attractive Chemotaxis Model

二、报告人：李彤 教授

三、时  间：2025年6月4日(周三) 15:00-16:00

四、地  点：闻理园A4-305

报告摘要：We prove the existence of moving spike patterns in an attractive chemotaxis model with small diffusion coefficient for the chemical. In the zero diffusion limit, ϵ → 0, we prove that the non-monotone traveling wave solutions of the system with ϵ > 0 converge to those of the system with ϵ = 0. Moreover, we show that the traveling wave solutions are linearly unstable. We perform numerical simulations and find existence of the moving spike patterns when ϵ > 0. We confirm that as ϵ → 0 the traveling wave solutions of the system with ϵ > 0 converge to the traveling wave solutions of the system with ϵ = 0.

Spike patterns in aggregating solutions are important in understanding how new capillaries sprout via angiogenesis from a preexisting vasculature in tumor angiogenesis.

This is a joint work with Casey Stone.

报告人简介：李彤，美国爱荷华(Iowa)大学数学系教授。1983年本科毕业于北京大学数学系，1992年于美国纽约大学柯朗研究所获博士学位，2008年担任美国爱荷华大学正教授，2008-2014年期间曾任西安交通大学、上海交通大学访问教授。目前主要从事非线性双曲守恒律、交通流、生物数学等方面的研究，尤其是在交通流和生物数学方面做了很多重要的工作。

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