Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions
type: Item
instance of: scholarly article
title: Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions
zbMATH Open document ID: 1470.35367
author: Yūki Naito
published in: Journal of Differential Equations
publication date: 2021-07-21T00:00:00Z
review text: The author derives criteria for global-in-time existence versus finite time blow-up of solutions for radially symmetric solutions of the minimal parabolic-elliptic Keller-Segel model of chemotaxis in the whole space \(\mathbb R^d\). They are expressed in terms of averaged initial data compared to averaged stationary solutions. The proofs are based on delicate monotonicity arguments. It is worth noting that conditions for the blow-up in dimensions \(3\le d\le 9\) differ from those for \(d\ge 10\) which reflects a different structure of the set of stationary solutions for such \(d\)'s.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35B06
zbMATH DE Number: 7373372
zbMATH Keywords: Keller-Segel model
zbMATH Keywords: radial solutions in higher dimensions
zbMATH Keywords: finite time blow-up
MaRDI profile type: Publication
full work available at URL: j.jde.2021.06.024
OpenAlex ID: W3175114880
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DOI: 10.1016/J.JDE.2021.06.024
description: scientific article; zbMATH DE number 7373372