Wavefront of an angiogenesis model

In this paper, we show the existence of traveling wave solutions to a chemotaxis model describing the initiation of angiogenesis. By a change of dependent variable, we transform the wave equation of the angiogenesis model to a Fisher type wave equation. Then we make use of the methods of analyzing the Fisher wave equation to obtain the existence of traveling wave solutions to the angiogenesis model. In virtue of the asymptotic behavior of the traveling wave solution at infinity, we find the explicit wave speed for cases of both zero and nonzero chemical diüsion. Finally based on the fact that the wave speed is convergent with respect to the chemical diüsion, we rigorously establish the zero chemical diüsion limit of traveling wave solutions by the energy estimates.