The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle
type: Item
instance of: scholarly article
zbMATH Open document ID: 1261.35080
DOI: 10.1137/110823584
author: Inwon Kim
author: Yao Yao
published in: SIAM Journal on Mathematical Analysis
publication date: 2012-08-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1102.0092
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 6070861
zbMATH Keywords: diffusion-aggregation model
zbMATH Keywords: finite speed of propagation
zbMATH Keywords: radially stationary solutions
zbMATH Keywords: compactly supported weak solutions
zbMATH Keywords: nonlocal aggregation term
zbMATH Keywords: degeneracy of the diffusion term
describes a project that uses: Chemotaxis
MaRDI profile type: Publication
OpenAlex ID: W2963320585
arXiv ID: 1102.0092
title: The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle
review text: The qualitative and asymptotic behavior of radially stationary solutions for a class of diffusion-aggregation equations is investigated. A universal estimate for compactly supported weak solutions is established. The challenge in the analysis consists of the nonlocal aggregation term as well as the degeneracy of the diffusion term, which generates compactly supported solutions. The key tools of the investigation of the considered problem are maximum-principle type arguments as well as estimates on mass concentration of solutions.
reviewed by: Mersaid Aripov
description: scientific article; zbMATH DE number 6070861