Asymptotic stability of traveling fronts to a chemotaxis model with nonlinear diffusion

Abstract

<p style='text-indent:20px;'>We are interested in the existence and stability of traveling waves of arbitrary amplitudes to a chemotaxis model with porous medium diffusion. We first make a complete classification of traveling waves under specific relations among the biological parameters. Then we show all these traveling waves are asymptotically stable under appropriate perturbations. The proof is based on a Cole-Hopf transformation and the energy method.</p>