Global solvability in a Keller-Segel-growth system with indirect signal production
type: Item
instance of: scholarly article
title: Global solvability in a Keller-Segel-growth system with indirect signal production
zbMATH Open document ID: 1501.92007
author: Guoqiang Ren
published in: Calculus of Variations and Partial Differential Equations
publication date: 2022-10-07T00:00:00Z
review text: The author studies a chemotaxis model with indirect signal production and reaction term \[ u_t=\Delta u-\chi\nabla\cdot(u\nabla v)+f(u), \] \[ \tau v_t=\Delta v-v+w, \] \[ \tau w_t=\Delta w-w+u, \] in bounded domains of \(\mathbb R^N\), with the homogeneous Neumann boundary conditions. Under the assumption \(\frac{f(s)}{s}\to-\infty\) as \(s\to\infty\) and \(f(0)\ge 0\), suitable generalized solutions are shown to to global-in-time. For a a generalized logistic term \(f(s)=\lambda s-\mu s^\kappa\) similar results are shown for \(\kappa \ge 2-\frac2N\) if \(N\ge 3\), and \(\kappa>1\) if \(N=2\).
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 7597567
zbMATH Keywords: chemotaxis
zbMATH Keywords: indirect signal production
zbMATH Keywords: reaction term
zbMATH Keywords: global solutions
MaRDI profile type: Publication
full work available at URL: s00526-022-02313-5
OpenAlex ID: W4295539711
Wikidata QID: Q114017782
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DOI: 10.1007/S00526-022-02313-5
description: scientific article; zbMATH DE number 7597567