  This paper is concerned with traveling wave solutions for a chemotaxis model
with degenerate diffusion of porous medium type. We establish the existence of
semi-finite traveling waves, including the sharp type and $C^1$ type
semi-finite waves. Our results indicate that chemotaxis slows down the wave
speed of semi-finite traveling wave, that is, the traveling wave speed for
chemotaxis with porous medium (degenerate) diffusion is smaller than that for
the porous medium equation without chemotaxis. As we know, this is a new result
not shown in the existing literature. The result appears to be a little
surprising since chemotaxis is a connective force. We prove our results by the
Schauder's fixed point theorem and estimate the wave speed by a variational
approach.
