Friday, November 18, 2022 — 12:00 pm — Laboratorio Zironi, edificio Matematica
Blow-up vs. global existence for some simplified chemotaxis models
Abstract: In this seminar we first introduce the Keller-Segel models (1970), largely used in mathematical biology to describe chemotaxis phenomena.
Chemotaxis is the movement of an organism (cells, bacteria) in response to a chemical stimulus; in this sense, the related mathematical formulation takes into account a coupled system of two PDEs: one for the cells’ density and the other for the chemical distribution. Two important issues are connected to these models: blow-up gathering processes (the cells concentrate at finite time in some spatial point) and temporal global behaviors (the cells indefinitely evolve in time without any coalescence tendency). We give some details for both phenomena in simplified situations.