Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 27, Issue 7, Pages 1327-1353Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202517400176
Keywords
Kinetic theory; active particles; parabolic scaling; hyperbolic scaling; multiscale methods
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Funding
- MIUR, Italian Minister for University and Research
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This paper develops a Hilbert type method to derive models at the macroscopic scale for large systems of several interacting living entities whose statistical dynamics at the microscopic scale is delivered by kinetic theory methods. The presentation is in three steps, where the first one presents the structures of the kinetic theory approach used toward the aforementioned analysis; the second step presents the mathematical method; while the third step provides a number of specific applications. The approach is focused on a simple system and with a binary mixture, where different time-space scalings are used. Namely, parabolic, hyperbolic, and mixed in the case of a mixture.
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