主讲人简介：

Michael Winkler，德国帕德博恩大学教授。1998年获德国帕德博恩大学理学学士学位，2000年获德国亚琛工业大学理学博士学位。毕业后留校任教，2008年起曾先后任德国杜伊斯堡-埃森大学、帕德博恩大学教授。研究方向为抛物型方程解的定性行为、耗散系统中奇点的自发形成以及交叉扩散系统等。在JEMS, Adv. Math, ARMA, JMPA, CMP等数学期刊上发表290余篇论文，被引20000余次；现担任M3AS，JDE等10多个国际高水平期刊编委。

内容摘要：

In its first part, this presentation revisits a basic question from parabolic regularity theory, and discusses some recent developments concerned with heat semigroup estimates and Gagliardo-Nirenberg interpolation involving certain Orlicz type expressions. An outcome of this is thereafter applied to a taxis-type parabolic modelfor the dynamics of microbial populations in nutrient-poor environments, containing some cross-degenerate diffusion mechanism as a core characteristic. The intention here is to outline an approach which, by relying on a result achieved in the first part in a crucial place, facilitates an appropriate control of such cross-degeneracies. In convex planar domains, this leads not only to a fairly comprehensive theory of global solvability, but also to a description of large time behavior and structure formation.