Speaker: Zhian Wang (IMA)
Title: Multi-scale approach in chemotaxis models
Abstract: This talk is focused on two questions of chemotaxis modeling. One is how to connect the macroscopic model with the microscopic mode. The other is how information in the microscopic model is passed onto the macroscopic model. For the first question, I use a non-perturbative approach to derive the parabolic limits of microscopic model and quickly get the desired macroscopic model. This approach has many advantages compared with conventional perturbation method. For the second question, I investigate the traveling waves of both microscopic and macroscopic models from which we can see how traveling waves in the microscopic model are retained, lost or created during the transition from the microscopic to macroscopic models. Biological implications will be discussed based on these result.