Modeling chemotaxis from $L^2$--closure moments in kinetic theory of active particles

Nicola Bellomo; Abdelghani Bellouquid; Juanjo Nieto; Juan Soler

doi:10.3934/dcdsb.2013.18.847

Article Contents

2013, Volume 18, Issue 4: 847-863. Doi: 10.3934/dcdsb.2013.18.847 open access

This issue Previous Article Preface: Special issue on cancer modeling, analysis and control Next Article Designing proliferating cell population models with functional targets for control by anti-cancer drugs

Modeling chemotaxis from $L^2$--closure moments in kinetic theory of active particles

1.
Department of Mathematica Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino
2.
University Cadi Ayyad, Ecole Nationale des Sciences Appliquées, Safi
3.
Departamento de Matemática Aplicada, Universidad de Granada

Received: February 29, 2012

Revised: April 30, 2012

Published: May 2013

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Abstract

This paper deals with the derivation of macroscopic tissue models from the underlying description delivered by a class of equations modeling binary mixtures of multi-cellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of biological functions and proliferative-destructive events. The analysis refers to a suitable hyperbolic approximation to show how the macroscopic tissue behavior can be described from the underlying cellular description. The approach is specifically focused on the modeling of chemotaxis phenomena by the Keller--Segel approximation.

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Mathematics Subject Classification: 35Q92, 92C17, 35K57.

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