Local well-posedness of kinetic chemotaxis models
type: Item
instance of: scholarly article
title: Local well-posedness of kinetic chemotaxis models
zbMATH Open document ID: 1158.35005
published in: Journal of Evolution Equations
publication date: 2008-09-22T00:00:00Z
review text: Using a semigroup approach, the local well-posedness is shown for a class of kinetic models of chemotaxis which describes the evolution of the distribution function \(f=f(t,x,v)\geq 0\) of cells at time \(t\geq 0\) and position \(x\in {\mathbb R}^N\) with velocity \(v\) in a compact subset \(V\) of \({\mathbb R}^N\) and the concentration of chemoattractant \(S=S(t,x)\geq 0\). The model couples a linear transport equation for \(f\) \[ \partial_{t}f + v \cdot \nabla_{x} f = {\mathcal T}[S] f \] with a parabolic equation for \(S\). The turning operator \({\mathcal T}[S]\) is an integral operator and describes how the velocities of the cells change, this process being biased by the chemoattractant concentration \(S\).
reviewed by: Philippe Laurençot
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 35F10
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 5345719
zbMATH Keywords: semigroup approach
zbMATH Keywords: linear transport equation
describes a project that uses: Chemotaxis
author: Sander Hille
MaRDI profile type: Publication
full work available at URL: s00028-008-0358-7
OpenAlex ID: W2098229212
DOI: 10.1007/S00028-008-0358-7
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description: scientific article; zbMATH DE number 5345719