Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation
type: Item
instance of: scholarly article
title: Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation
zbMATH Open document ID: 1475.35060
author: Masaaki Mizukami
author: Tatsuhiko Ono
author: Tomomi Yokota
published in: Journal of Differential Equations
publication date: 2020-01-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1903.00124
review text: This paper deals with a quasilinear degenerate chemotaxis system with flux limitation, under no-flux boundary conditions in the balls, and the initial condition for a radially symmetric and positive initial data. \textit{N. Bellomo} and \textit{M. Winkler} [Commun. Partial Differ. Equations 42, No. 3, 436--473 (2017; Zbl 1430.35166)] proved local existence of unique classical solutions and extensibility criterion ruling out gradient blow-up as well as global existence and boundedness of solutions when \(p=q=1\) under some conditions. This paper derives local existence and extensibility criterion ruling out gradient blow-up when \(p,q\ge 1\), and moreover shows global existence and boundedness of solutions when \(p>q+1-\frac{1}{n}\).
reviewed by: Yuanyuan Ke
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 7151381
zbMATH Keywords: degenerate chemotaxis system
zbMATH Keywords: flux limitation
zbMATH Keywords: extensibility criterion
zbMATH Keywords: boundedness
zbMATH Keywords: elliptic-parabolic system
MaRDI profile type: Publication
OpenAlex ID: W2963693172
arXiv ID: 1903.00124
cites work: Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
cites work: A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up
cites work: Finite-time blow-up in a degenerate chemotaxis system with flux limitation
cites work: Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces
cites work: Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation
cites work: Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
cites work: Finite-time blowup in a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 2
cites work: New critical exponents in a fully parabolic quasilinear Keller-Segel system and applications to volume filling models
cites work: Finite-time blow-up in a quasilinear system of chemotaxis
cites work: Finite-time blow-up for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
cites work: Blow-up in a chemotaxis model without symmetry assumptions
cites work: An iterative approach to \(L^\infty\)-boundedness in quasilinear Keller-Segel systems
cites work: Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
cites work: Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
cites work: Boundedness in a quasilinear fully parabolic Keller-Segel system via maximal Sobolev regularity
cites work: Initiation of slime mold aggregation viewed as an instability
cites work: Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system
cites work: Boundedness in a chemotaxis-haptotaxis model with nonlinear diffusion
cites work: Q4381941
cites work: Q4824324
cites work: Q4659860
cites work: Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
cites work: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
cites work: Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
cites work: Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
cites work: Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect
Wikidata QID: Q127811277
DOI: 10.1016/J.JDE.2019.05.026
description: scientific article