讲座主题：The Existence of Moving Spike Patterns in an Attractive Chemotaxis Model

专家姓名：李彤

工作单位：美国爱荷华大学

讲座时间：2025年07月01日 15:30-16:30

讲座地点：数学院大会议室341

主办单位：烟台大学数学与信息科学学院

内容摘要：

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.

主讲人介绍：

李彤，美国爱荷华大学数学系教授。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。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。