講座主題：The Existence of Moving Spike Patterns in an Attractive Chemotaxis Model
專(zhuān)家姓名：李彤
工作單位：美國(guó)愛(ài)荷華大學(xué)
講座時(shí)間：2025年07月01日 15:30-16:30
講座地點(diǎn)：數(shù)學(xué)院大會(huì)議室341
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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, ? → 0, we prove that the non-monotone traveling wave solutions of the system with ? > 0 converge to those of the system with ? = 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 ? > 0 . We confirm that as ? → 0 the traveling wave solutions of the system with ? > 0 converge to the traveling wave solutions of the system with ? = 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.
主講人介紹：
李彤，美國(guó)愛(ài)荷華大學(xué)數(shù)學(xué)系教授。1983年本科畢業(yè)于北京大學(xué)數(shù)學(xué)系，1992年于美國(guó)紐約大學(xué)柯朗研究所獲博士學(xué)位，2008年擔(dān)任美國(guó)愛(ài)荷華大學(xué)正教授。目前主要從事非線(xiàn)性雙曲守恒律、交通流、生物數(shù)學(xué)等方面的研究，尤其是在交通流和生物數(shù)學(xué)方面做了很多重要的工作。
