| Gagliardo-Nirenberg interpolation in Orlicz spaces near L^1 and applications to parabolic smoothing and doubly degenerat |
| 发布人:曾铮 发布时间:2026-10-22 浏览次数:10 |
|
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. |