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

 School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P.R.China

* Corresponding author: zhangkj201@nenu.edu.cn

Received  August 2020 Revised  November 2020 Published  January 2021

Fund Project: The third author is supported by National Science Foundation of China (No. 11771071)

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.

Citation: Mohammad Ghani, Jingyu Li, Kaijun Zhang. Asymptotic stability of traveling fronts to a chemotaxis model with nonlinear diffusion. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021017
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