期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 23, 期 14, 页码 2647-2670出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202513500425
关键词
Swarming; asymptotic analysis; traveling wave solutions
资金
- Polish Ministry of Science and Higher Education [N201 362536]
- National Scientific Centre of Poland [N201 605640]
- [N N201 362536]
In the present paper we study the macroscopic limits of a kinetic model for interacting entities (individuals, organisms, cells). The kinetic model is one-dimensional and the entities are characterized by their position and orientation (+/-) with swarming interaction controlled by a sensitivity parameter. The macroscopic limits of the model are considered for solutions close either to the diffusive (isotropic) or to the aligned (swarming) equilibrium states for various values of that parameter. In the former case the classical linear diffusion equation results whereas in the latter a traveling wave solution does both in the zeroth (Euler) and first (Navier-Stokes) order of approximation.
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