报告一: Blow-up profile for the parabolic-elliptic Keller-Segel system in whole space with dimension n>2  

报告人: 白学利  西北工业大学

时  间:  2020.12.14 2:30-3:30

地  点: 腾讯会议 ID：578 742 650

报告简介:  Recently, P. Souplet and M. Winkler [CMP, 2019] studied a simplified parabolic-elliptic Keller-Segel system in $\Omega\subset R^n (n>2)$. They obtained the blow-up profile $cr^{-2}\le U(r) \le Cr^{-2}$ under suitable conditions, where  $U(r)=\lim_{t\rightarrow T}u(r,t)$. An open problem proposed in this paper is that, the solution admits a exactly profile: $r^2 U(r)$ converges to some constant as $r$ goes to zero. In this talk, we mainly discuss how to solve this open problem when the domain is the whole space.  

报告人简介：白学利，西北工业大学理学院副教授，2012年4月在大连理工大学获得博士学位。2012年9月-2015年6月在华东师范大学偏微分方程中心跟随倪维明教授进行博士后研究。2017年5月-2018年10月受洪堡基金资助在德国帕德博恩大学同数学家Michael Winkler进行合作研究。目前主要关注偏微分方程在生物数学中的应用，研究解的稳定性以及长时间行为等定性性质。 在J. Functional Analysis, Calc. Var&PDE, Indiana Univ. Math. J., J. Differential Equations, Proceedings of AMS等数学期刊发表论文十余篇，主持国家自然科学基金青年项目，中国博士后基金一等资助，中国博士后特别资助各一项，参与国家自然科学基金重点项目一项,面上项目两项。

报告二: Spreading properties of the farmer and hunter-gatherer model（I）  

报告三: Spreading properties of the farmer and hunter-gatherer model（II）  

报告人: 萧冬远  法国蒙彼利埃大学

时  间:   2020.12.14  3:40-5:50

地  点: 腾讯会议 ID：578 742 650

报告简介：In this lecture, we investigate the spreading properties of solutions of farmer and hunter-gatherer model which is a three-component reaction-diffusion system. Ecologically, the model describes the geographical spreading of an initially localized population of farmers into a region occupied by hunter-gatherers. This model was proposed by Aoki, Shida and Shigesada in 1996. By numerical simulations and some formal linearization arguments, they concluded that there are four different types of spreading behaviors depending on the parameter values. Despite such intriguing observations, no mathematically rigorous studies have been made to justify their claims. The main difficulty comes from the fact that the comparison principle does not hold for the entire system. In this lecture, we give theoretical justification to all of the four types of spreading behaviors observed by Aoki et al.. Furthermore, we show that a logarithmic phase drift of the front position occurs as in the scalar KPP equation.

报告人简介：萧冬远，2019年于日本东京大学数学系毕业。此后在日本明治大学的MIMS应用数学研究所从事研究工作一年半。2020年10月开始于法国蒙彼利埃大学的IMAG数学研究所从事研究工作。主要研究领域是以生物生态学为背景的抛物方程的数学解析。