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

Mohammad Ghani; Jingyu Li; Kaijun Zhang

doi:10.3934/dcdsb.2021017

Article Contents

2021, Volume 26, Issue 12: 6253-6265. Doi: 10.3934/dcdsb.2021017 open access

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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
^* Corresponding author: zhangkj201@nenu.edu.cn

Received: July 31, 2020

Revised: October 31, 2020

Early access: January 2021

Published: December 2021

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 35A01, 35B40, 35Q92; Secondary: 92C17.

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