|Department of Math, The University of Iowa
We study global existence and long-time behavior of solutions for hyperbolic-parabolic PDE models of chemotaxis. We show the existence and the stability of traveling wave solutions to a system of nonlinear conservation laws derived from the Keller-Segel model.
Traveling wave solutions of chemotaxis models with growth are also investigated. Moreover, we find oscillatory traveling wave solutions to an attractive chemotaxis system which are biologically relevant.