A Kinetic Flocking Model with Diffusion
Publication in refereed journal

Times Cited
Web of Science83WOS source URL (as at 17/09/2020) Click here for the latest count
Altmetrics Information

Other information
AbstractWe study the stability of the equilibrium states and the rate of convergence of solutions towards them for the continuous kinetic version of the Cucker-Smale flocking in presence of diffusion whose strength depends on the density. This kinetic equation describes the collective behavior of an ensemble of organisms, animals or devices which are forced to adapt their velocities according to a certain rule implying a final configuration in which the ensemble flies at the mean velocity of the initial configuration. Our analysis takes advantage both from the fact that the global equilibrium is a Maxwellian distribution function, and, on the contrary to what happens in the Cucker-Smale model (IEEE Trans Autom Control 52:852-862, 2007), the interaction potential is an integrable function. Precise conditions which guarantee polynomial rates of convergence towards the global equilibrium are found.
All Author(s) ListDuan RJ, Fornasier M, Toscani G
Journal nameCommunications in Mathematical Physics
Volume Number300
Issue Number1
PublisherSpringer Verlag (Germany)
Pages95 - 145
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesPhysics; Physics, Mathematical; PHYSICS, MATHEMATICAL

Last updated on 2020-18-09 at 00:53