Eventual smoothness and asymptotic behaviour of solutions to a chemotaxis system perturbed by a logistic growth
type: Item
instance of: scholarly article
title: Eventual smoothness and asymptotic behaviour of solutions to a chemotaxis system perturbed by a logistic growth
zbMATH Open document ID: 1409.35046
author: G. Viglialoro
author: Thomas E. Woolley
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2018-12-27T00:00:00Z
review text: The parabolic chemotaxis system with logistic-type source and homogeneous Neumann conditions is studied in convex domains of \({\mathbb R}^n\), \(n\geq 1\). The existence of very weak global in time solutions is shown, as well as the boundedness and regularity (for large time) of solutions are studied. Illustrations of dynamics of the system are given for \(n\leq 3\) by means of numerical simulations.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35K59
zbMATH DE Number: 6996819
zbMATH Keywords: logistic source
zbMATH Keywords: boundedness of solutions
zbMATH Keywords: homogeneous Neumann conditions
zbMATH Keywords: convex domains
MaRDI profile type: Publication
full work available at URL: dcdsb.2017199
OpenAlex ID: W2739679666
cites work: LOWER ESTIMATE OF THE ATTRACTOR DIMENSION FOR A CHEMOTAXIS GROWTH SYSTEM
cites work: Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
cites work: Modelling biological invasions: individual to population scales at interfaces
cites work: Finite-time blow-up in a quasilinear system of chemotaxis
cites work: On explicit lower bounds and blow-up times in a model of chemotaxis
cites work: Blow-up in a chemotaxis model without symmetry assumptions
cites work: Boundedness vs. blow-up in a chemotaxis system
cites work: On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
cites work: Initiation of slime mold aggregation viewed as an instability
cites work: Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source
cites work: Lower bounds for blow-up in a parabolic-parabolic Keller-Segel system
cites work: Blow‐up phenomena in chemotaxis systems with a source term
cites work: Blow-up of a general Keller-Segel system with source and damping terms
cites work: Mathematical biology. Vol. 2: Spatial models and biomedical applications.
cites work: Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
cites work: Exponential attractor for a chemotaxis-growth system of equations
cites work: Q4824324
cites work: Spatio-temporal chaos in a chemotaxis model
cites work: Lower bounds for blow-up in a model of chemotaxis
cites work: Inequalities and Convexity
cites work: Hölder estimates for local solutions of some doubly nonlinear degenerate parabolic equations
cites work: Boundedness in a chemotaxis model with oxygen consumption by bacteria
cites work: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
cites work: A Chemotaxis System with Logistic Source
cites work: Q5253796
cites work: Blow-up time of a Keller-Segel-type system with Neumann and Robin boundary conditions.
cites work: Very weak global solutions to a parabolic-parabolic chemotaxis-system with logistic source
cites work: Boundedness properties of very weak solutions to a fully parabolic chemotaxis-system with logistic source
cites work: Chemotaxis with logistic source: very weak global solutions and their boundedness properties
cites work: Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
cites work: Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
cites work: Does a ‘volume-filling effect’ always prevent chemotactic collapse?
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
DOI: 10.3934/DCDSB.2017199
description: scientific article; zbMATH DE number 6996819