Asymptotic behaviors and existence of traveling wave solutions to the Keller-Segel model with logarithmic sensitivity
type: Item
instance of: scholarly article
title: Asymptotic behaviors and existence of traveling wave solutions to the Keller-Segel model with logarithmic sensitivity
zbMATH Open document ID: 1505.35041
author: Yanyan Li
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2022-11-23T00:00:00Z
review text: This paper is concerned with the existence of traveling wave solutions for the Keller-Segel model with logarithmic sensitivity. By the Hopf-Cole transformation and traveling wave transformation, the degenerate Keller-Segel system is transformed into a singularly perturbed system. By constructing an invariant region to prove the existence of the traveling wave solutions for the degenerate system, the author obtains the traveling wave solutions for the Keller-Segel system with small parameters by means of geometric singular perturbation theory and Fredholm theory. Finally, the asymptotic behaviour of the travelling wave solutions is discussed.
reviewed by: L. Shangerganesh
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 7622282
zbMATH Keywords: Keller-Segel model
zbMATH Keywords: traveling wave solutions
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: geometric singular perturbation
zbMATH Keywords: invariant manifold
zbMATH Keywords: Hopf-Cole transformation
MaRDI profile type: Publication
full work available at URL: dcdsb.2022146
OpenAlex ID: W4288082064
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DOI: 10.3934/DCDSB.2022146
description: scientific article; zbMATH DE number 7622282