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ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES

N. BELLOMO

Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy

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A. BELLOUQUID

University Cadi Ayyad, Ecole Nationale des Sciences Appliquées, Safi, Maroc

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J. NIETO

University of Granada, Departamento de Matemática Aplicada, 18071 Granada, Spain

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, and

J. SOLER

University of Granada, Departamento de Matemática Aplicada, 18071 Granada, Spain

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https://doi.org/10.1142/S0218202512005885Cited by:78 (Source: Crossref)

Abstract

This paper proposes a review and critical analysis of the asymptotic limit methods focused on the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis deals with suitable parabolic, hyperbolic, and mixed limits. The review includes the derivation of the classical Keller–Segel model and flux limited models that prevent non-physical blow up of solutions.

Keywords:

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