Speaker: Thomas Hillen (University of Alberta)
Title: A user's guide to PDE models for chemotaxis
Abstract: The mathematical analysis of chemotaxis (the movement of biological cells or organisms in response to chemical gradients) has developed into a large and diverse discipline. A simplified version of the original Keller-Segel model (called "minimal model") displays already self-aggregation properties, which are expressed, in higher dimensions, through finite time blow-up solutions.
Based on this "minimal" model we study modifications and variations of chemotaxis models. These variations are partly motivated through biological realism and partly through mathematical convenience. We will present results on global existence and blow-up for the modified models and discuss spatial pattern formation for those models with global solutions. Typical patterns show an interesting merging and emerging dynamics. (joint work with Kevin Painter, Heriot Watt, Edinburgh)