Description
We consider a class of Keller-Segel systems under Laplacian form, which models chemotactic aggregation with local sensing. We will see that while reminiscent of the classical (minimal) Keller-Segel system, which may exhibit blow-up in finite time, this class of system typically possesses global-in-time solutions. We discuss its rich long-time behaviour and, if time permits, possible extensions in presence of nonlinear self-diffusion.