Wavefront of an angiogenesis model (Q713242)

The author considers the traveling wave solutions to a chemotaxis model. The author first converts the chemotaxis model to a Fisher type wave equation. Then by making use of the results on Fisher wave equations, the existence of traveling wave solutions to chemotaxis model is proved, which removes a small assumption on \(\varepsilon\) in a known result. By applying the asymptotic behavior of the traveling wave solution at infinity, the author finds the explicit wave speed in the case of zero and nonzero chemical diffusion. Finally, the author rigorously deduces the zero chemical diffusion limit of the traveling wave solutions by energy arguments.