Global existence and boundedness of a chemotaxis model with indirect production and general kinetic function
type: Item
instance of: scholarly article
title: Global existence and boundedness of a chemotaxis model with indirect production and general kinetic function
zbMATH Open document ID: 1450.35066
author: Xie Li
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2020-07-07T00:00:00Z
review text: The author considers a chemotaxis model \[ \begin{cases} u_{t} =\Delta u+\chi \nabla \cdot (u\nabla v)+f(u), &x\in \Omega ,\ t>0, \\ v_{t} =\Delta v-v+w, &x\in \Omega ,\ t>0, \\ \tau w_{t}+\lambda w =g(u), &x\in \Omega ,\ t>0, \end{cases} \] in a bounded domain \(\Omega \) with a regular boundary, \(\Omega \subset \mathbb{R}^{n}\), \(n\leq 3\), where \(\chi ,\tau ,\lambda \) are positive parameters, and \(f\) and \(g\) are known functions. The purpose of the paper is to check if the solution to the model is global and bounded for certain general functions \(f\) and \(g\). The author provides in two main theorems explicit conditions relating the functions \(f,g\), the model parameters and the initial data, which ensure the global-in-time existence and uniform boundedness for the corresponding 2D and 3D Neumann boundary value problem. In particular, for \(f\equiv 0\) and \(g\) a linear function, the global bounded classical solution to the corresponding 2D Neumann initial-boundary value problem with arbitrarily large initial data and chemotactic sensitivity is established.
reviewed by: Gabriela Marinoschi
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35K51
zbMATH DE Number: 7218126
zbMATH Keywords: indirect signal production
zbMATH Keywords: 2D Neumann boundary value problem
zbMATH Keywords: 3D Neumann boundary value problem
MaRDI profile type: Publication
full work available at URL: s00033-020-01339-z
OpenAlex ID: W3039280879
cites work: Pattern formation in a model for mountain pine beetle dispersal: linking model predictions to data
cites work: Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier–Stokes system modeling coral fertilization
cites work: Global classical solutions in a Keller-Segel(-Navier)-Stokes system modeling coral fertilization
cites work: Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
cites work: Q4381941
cites work: Q4398321
cites work: Blow-up in a chemotaxis model without symmetry assumptions
cites work: Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
cites work: Exponential attractor for a chemotaxis-growth system of equations
cites work: Q4824324
cites work: Q4459642
cites work: Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system
cites work: Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
cites work: How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?
cites work: Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source
cites work: Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system
cites work: On a fully parabolic chemotaxis system with nonlinear signal secretion
cites work: To the exclusion of blow-up in a three-dimensional chemotaxis-growth model with indirect attractant production
cites work: Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production
cites work: Application of an Adams type inequality to a two-chemical substances chemotaxis system
cites work: Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion
cites work: Global solution for a chemotactic–haptotactic model of cancer invasion
cites work: A Chemotaxis-Haptotaxis Model: The Roles of Nonlinear Diffusion and Logistic Source
cites work: Q5630031
cites work: Q5547721
cites work: Boundedness vs. blow-up in a chemotaxis system
cites work: On the global existence of solutions to an aggregation model
cites work: Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
cites work: Nondegeneracy of blow-up points for the parabolic Keller-Segel system
cites work: Distributions, Sobolev spaces, elliptic equations
DOI: 10.1007/S00033-020-01339-Z
description: scientific article; zbMATH DE number 7218126