Speaker: Michael Winkler

Time: 17:00-18:00 pm, April 1, 2023, GMT+8

Venue: Zoom Meeting ID: 835 6104 9315 Passcode: 004084

Abstract:

In mathematical biology, chemotaxis terms partially oriented movement of individuals - usually of single cells - along gradients of a  chemical signal substance. Experimental findings report striking  effects of such chemotactic migration, inter alia phenomena of  self-organization such as spatial aggregation. A prototypical model for the description of such chemotactic dynamics,  consisting of two parabolic equations with a cross-diffusive term as  its most characteristic ingredient, was proposed by Keller and Segel  in 1970 already and intensively discussed since then in the  mathematical literature. However, fundamental mathematical questions,  particularly concerning the spontaneous emergence of large densities  and cell aggregates, could only be answered satisfactorily for  simplified systems up to now.The presentation aims at reporting some recent developments with  regard to the detection of blow-up phenomena.

Source: School of Mathematical Sciences