题目：Traveling wave solutions for a chemotaxis model with nonlinear chemical gradient
报告人：艾尚兵 教授，University of Alabama in Huntsville
Abstract：”Mathematical modelling of chemotaxis (the movement of biological cells or organisms in response to chemical gradients) has developed into a large and diverse discipline, whose aspects include its mechanistic basis, the modelling of speciﬁc systems and the mathematical behavior of the underlying equations. The Keller-Segel model of chemotaxis has provided a cornerstone for much of this work, its success being a consequence of its intuitive simplicity, analytical tractability and capacity to replicate key behavior of chemotactic populations.” (T. Hillen and K. J. Pinter in J. Math. Biology 2008). In particular, traveling wave solutions of the Keller-Segel model have been successfully studied for the lab observed phenomenon: bands of motile bacteria Escherichia coli travel at constant speed when the bacteria are placed in one end of a capillary tube containing oxygen and an energy source.
In this talk we discuss the traveling wave solutions for a generalized Keller-Segel chemotaxis model with nonlinear chemical gradient. The nonlinear (bounded) chemical gradient accounts for the fact that cells have maximum motile velocity. Using the geometric singular perturbation theory and phase plane analysis, we establish the existence of traveling wave solutions for this model. Such a result further demonstrates traveling wave patterns driven by chemotactic mechanisms.