Deadcore behavior in chemotaxis systems with nonlinear diffusion

Many chemotaxis models have been proposed to mathematically capture the visible patterns arising in physical experiments. Patterns in the population, however, are only partially described by the areas where self-organized accumulation of cells happens. Regions featuring a complete absence of cells also contribute quite clearly to any detectable pattern. These regions are typically called \emph{dead-cores} and their behavior provides information on possible patterns arising during the evolution.

After revisiting known results on global solutions and their long-term dynamics to some chemotaxis systems, we will take an in-depth look at the dead-core behavior in closely related chemotaxis systems featuring nonlinear diffusion.