[Mini Courses] The role of degeneracies in the analysis of chemotaxis systems. Lectures #3 and #4

时   间：  2023-03-29 15:45 — 17:45

Lecture #3: Explicit degeneracies at small densities
Abstract:
In situations in which populated regions themselves are to be characterized, the inclusion of diffusion mechanisms involving degeneracies at small population densities constitutes a classical refinement in parabolic modeling of population dynamics.It is here to be discussed how far the additional presence of taxis mechanisms may lead to novel effects. In particular, it will be sketched how an appropriately designed comparison arguments can reveal taxis-driven persistent localization of solutions.
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Lecture #4: Cross-degeneracies: Reduced motility at large signal densities
Abstract:
Especially when local sensing mechanisms are involved, appropriate modeling requires the use of taxis-type systems which account for suitable inhibition of migration at large densities of the respective signal concentration. Results on global solvability and on singularity formation will be reprted on, as well as some challenges and possibilities related to corresponding analysis.