期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 26, 期 11, 页码 2041-2069出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202516400078
关键词
Kinetic theory; active particles; cross-diffusion; multiscale methods
资金
- MIUR, Italian Minister for University and Research, PRIN Project
- Hassan II, Academy of Sciences and Technology (Morocco)
This paper deals with a micro-macro derivation of a variety of cross-diffusion models for a large system of active particles. Some of the models at the macroscopic scale can be viewed as developments of the classical Keller-Segel model. The first part of the presentation focuses on a survey and a critical analysis of some phenomenological models known in the literature. The second part is devoted to the design of the micro-macro general framework, where methods of the kinetic theory are used to model the dynamics of the system including the case of coupling with a fluid. The third part deals with the derivation of macroscopic models from the underlying description, delivered within a general framework of the kinetic theory.
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