Travelling front solutions arising in the chemotaxis-growth model
type: Item
instance of: scholarly article
title: Travelling front solutions arising in the chemotaxis-growth model
zbMATH Open document ID: 1106.35119
DOI: 10.4171/IFB/141
author: Mitsuo Funaki
author: Masayasu Mimura
author: Tohru Tsujikawa
published in: Interfaces and Free Boundaries
publication date: 2006-11-21T00:00:00Z
review text: Using a singular limit procedure the authors study the dynamics of growth patterns in the bistable reaction-diffusion-advection system of biological species subjected to diffusion and chemotaxis \[ \frac{\partial u}{\partial t}=d_u\triangle u-\nabla (u\nabla\chi(v))+f(u),\; \frac{\partial v}{\partial t}=d_v\triangle v+\alpha u-\beta v,t>0,\;\chi\in \mathbb{R}^2. \] Here \(u(t,x)\) is their density and \(v(t,x)\) is the concentration of a chemical attractant, \(d_u\) and \(d_v\) are the diffusion rates of \(u\) and \(v\), \(\chi(v)\) is the chemostatic sensitivity function of the chemical attractant, \(\chi'(v)>0\) for \(v>0\). The dependence of pattern shapes on the measure \(k\) of the intensity of the chemotactic effect is also studied numerically.
Mathematics Subject Classification ID: 35Q80
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 5074419
zbMATH Keywords: chemotaxis
zbMATH Keywords: travelling front
zbMATH Keywords: singular perturbation
zbMATH Keywords: interfacial stability
zbMATH Keywords: reaction-diffusion-advection system
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/ifb/141
OpenAlex ID: W2036425323
description: scientific article; zbMATH DE number 5074419