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 C1 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 convective force. We prove our results by the Schauder’s fixed point theorem and estimate the wave speed by a variational approach.
|Number of pages||19|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - Oct 2021|
ASJC Scopus subject areas
- Applied Mathematics