Journal article
Traveling wave solutions of a singular Keller-Segel system with logistic source
Mathematical biosciences and engineering : MBE, Vol.19(8), pp.8107-8131
06/01/2022
DOI: 10.3934/mbe.2022379
Abstract
This paper is concerned with the traveling wave solutions of a singular Keller-Segel system modeling chemotactic movement of biological species with logistic growth. We first show the existence of traveling wave solutions with zero chemical diffusion in $ \mathbb{R} $. We then show the existence of traveling wave solutions with small chemical diffusion by the geometric singular perturbation theory and establish the zero diffusion limit of traveling wave solutions. Furthermore, we show that the traveling wave solutions are linearly unstable in the Sobolev space $ H^1(\mathbb{R}) \times H^2(\mathbb{R}) $ by the spectral analysis. Finally we use numerical simulations to illustrate the stabilization of traveling wave profiles with fast decay initial data and numerically demonstrate the effect of system parameters on the wave propagation dynamics.
Details
- Title: Subtitle
- Traveling wave solutions of a singular Keller-Segel system with logistic source
- Creators
- Tong Li - University of IowaZhi-An Wang - Hong Kong Polytechnic University
- Resource Type
- Journal article
- Publication Details
- Mathematical biosciences and engineering : MBE, Vol.19(8), pp.8107-8131
- DOI
- 10.3934/mbe.2022379
- eISSN
- 1551-0018
- Publisher
- AIMS Press
- Language
- English
- Date published
- 06/01/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984269359902771
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