期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 27, 期 6, 页码 1153-1175出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202517400115
关键词
Blow-up; global existence; kinetic equations; swarms
In this paper we study a kinetic equation that describes swarm formations. The right-hand side of this equation contains nonlinear integro-differential terms responsible for two opposite tendencies: dissipation and swarming. The nonlinear integral operator describes the changes of velocities (orientations) of interacting individuals. The interaction rate is assumed to be dependent of velocities of interacting individuals. Although the equation seems to be rather simple it leads to very complicated dynamics. In this paper, we study possible blow-ups versus global existence of solutions and provide results on the asymptotic behavior. The complicated dynamics and possibility of blow-ups can be directly related to creation of swarms.
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