Lecture: "Dynamics of a chemotaxis system with indirect signal production"

Lecturer: Philippe Laurencot, Université de Toulouse
Host: Prof. M. Burger

Abstract: The well-posedness of a chemotaxis system with indirect signal production in a two-dimensional domain is shown, all solutions being global unlike the classical Keller-Segel chemotaxis system. Nevertheless, there is a threshold value M_c of the mass of the first component which separates two different behaviours: solutions are bounded when the mass is below M_c while there are unbounded solutions starting from initial conditions having a mass exceeding M_c. This result extends to arbitrary two-dimensional domains a previous result of Tao & Winkler (2017) obtained for radially symmetric solutions to a simplified version of the model in a ball and relies on a different approach involving a Liapunov functional.