报告题目: Finite-time blow-up in the Keller-Segel system
报告人：Michael Winkler教授（德国Paderborn 大学）
In mathematical biology, chemotaxis terms partially oriented movement of individuals - usually of single cells - along gradients of a chemical signal substance. Experimental findings report striking affects of such chemotactic migration, inter alias phenomena of self-organization such as spatial aggregation. A prototypical model for the description of such chemotactic dynamics, consisting of two parabolic equations with a cross-diffusive term as its most characteristic ingredient, was proposed by Keller and Segel in 1970 already and intensively discussed since then in the mathematical literature. However, the fundamental mathematical question concerning the existence of exploding solutions could only be answered satisfactorily for simplified systems up to now. The presentation aims at reporting some recent developments, with a particular focus on mathematical methods for detecting blow-up solutions.
Michael Winkler，德国Paderborn大学教授，2000年在亚琛工业大学（RWTH Aachen）获得博士学位；主要从事偏微分方程的研究，特别是在抛物型偏微分方程方面做出了突出贡献；已在Arch Rational Mech Anal、J European Math Soc、Trans Amer Math Society、SIAM J Math Anal、J Differential Eq、Math Models Methods Appl Sci、Math. Ann等国际一流数学期刊上发表学术论文90余篇，SCI论文被引用1000余次；现任Mathematical Models and Methods in Applied Sciences、Discrete and Continuous Dynamical Systems - Ser B、Nonlinear Analysis: Real World、Journal of Mathematical Analysis and Applications、Acta Applicandae Mathematicae等高水平SCI学术期刊编委