[Mini Courses] [Mini Courses] The role of degeneracies in the analysis of chemotaxis systems. Lectures #5 and #6

时   间：  2023-03-31 15:45 — 17:45

Lecture #5: Cross-degeneracies at small signal densities: existence theory
Abstract:
Striking experiments have revealed considerably colorful behavior in populations of primitive bacteria when exposed to nutrient-poor environments. As a core element, models for an adequate description contain diffusion degeneracies at small densities of the directing signal. It is to be described how resulting challenges already for basic solution theories can be dealt with.
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Lecture #6: Cross-degeneracies at small signal densities: qualitative behavior
Abstract:
It is intended to outline how variational methods can be used to derive statements on qualitative behavior in models of the form introduced in Lecture #5. A particular focus will be on techniques capable of asserting large time stabilization, and on uncovering some remarkable stability features genuinely due to the considered type of cross-degeneracies.