The Existence Of Traveling Waves In A Volume-filling Chemotaxis Model

In this paper we mainly studied the existence of traveling waves in a volume-filling chemotaxis model. First,we get the existence of ut=d1uxx+μu(1-u)(u一α)by the existence of traveling waves in ut=uxx+u(1-u)(u-α).Then we can prove the existence of traveling waves inWe assume the wavefront can be approximated by the wavefront of that question.Then we use Banach fixed point theorem to prove it. Finally we get the existence of traveling waves in this volume-filling chemotaxis model,There is a bistable growth μu(1-u)(u-α)in that model.Because of the particular-ity of bistable growth,we get the existence of different kinds of traveling waves in this paper.