Chemotaxis systems with logistic source: Boundedness, blow-up and global generalised solvability

This talk addresses the qualitative behaviour of solutions to Keller–Segel systems incorporating superlinear degradation terms, which describe the aggregation of organisms in response to chemical signals while accounting for population growth.

We show (both for the fully parabolic system as well as for certain parabolic–elliptic simplifications) that solutions are always globally bounded if the logistic-type degradation is sufficiently strong while certain weaker but still superlinear dampening terms still allow for solutions blowing up in finite time. This is then complemented by findings stating that very mild assumptions suffice to guarantee the global existence of generalised solutions.