[Mini Courses] The role of degeneracies in the analysis of chemotaxis systems. Lectures #1 and #2

时   间：  2023-03-27 15:45 — 17:45

Lecture #1: Implicit diffusion degeneracies in classical Keller-Segel systems
Abstract:
Already in classical Keller-Segel systems, in frameworks of radial solutions the interplay of taxis and diffusion can be viewed as the competition between a Burgers-type transport mechanism and a diffusion process involving certain space-dependent degeneracies. Possible implications on solution behavior will be described, and methods for analytical descriptions will be discussed; a special focus will be on blow-up arguments based on the use of moment-like functionals.
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Lecture #2: Explicit degeneracies at large densities
Abstract:
In various application contexts, reduced motilities of individuals in crowded regions are of significant relevance. Adequately accounting for this may require the inclusion of explicitly present degeneracies of the migration operators
at large densities. Some analytical techniques to adequately describe the resulting more complex taxis-diffusion interaction are to be outlined, especially hightlighting the role of appropriate comparison arguments.