Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 847 - 863, Volume 18, Issue 4, June 2013      doi:10.3934/dcdsb.2013.18.847

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Nicola Bellomo - Department of Mathematica Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email)
Abdelghani Bellouquid - University Cadi Ayyad, Ecole Nationale des Sciences Appliquées, Safi, Morocco (email)
Juanjo Nieto - Departamento de Matemática Aplicada, Universidad de Granada, Spain (email)
Juan Soler - Departamento de Matemática Aplicada, Universidad de Granada, Spain (email)

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.

Keywords:  Living systems, cancer cells, chemotaxis, kinetic theory, multi-cellular systems, closure method, Keller--Segel.
Mathematics Subject Classification:  35Q92, 92C17, 35K57.

Received: March 2012;      Revised: May 2012;      Available Online: February 2013.