Mathematics of Chemotactic Traveling Waves with Logarithmic Sensitivity

Dr. Zhian Wang

Department of Mathematics
The Hong Kong Polytechnic University, Hong Kong, China

9 November 2011
Shelby Center 158
2:30 (Refreshements at 2:00)

Abstract

In this talk, we will discuss traveling wave solutions for a class of chemotaxis models with logarithmic sensitivity, which may describe a variety of biological/medical phenomena including bacterial chemotactic motion, initiation of angiogenesis and reinforced random walks. The challenges of analyzing traveling wave solutions of such type of chemotaxis model lie in the high dimensionality and the singularity. Hence the routine approaches, such as phase plane analysis, no longer work. In the talk, we shall show these challenges can be resolved by variable transformations, such that the transformed system can be solved by the regular approaches. The existence, wave speed and stability of traveling wave solutions will be discussed and open questions will be presented.