期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 22, 期 1, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202512005885
关键词
Living systems; kinetic theory; multicellular systems; chemotaxis; asymptotic limits; hyperbolic limits; diffusion limits
资金
- European Union [FP7-HEALTH-F4-2008-202047-RESOLVE]
- Ministerio de Ciencia e Innovacion (Spain) [MTM2008-05271]
- Junta de Andalucia [P08-FQM-4267]
- Academie Hassan II
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.
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