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Kinetic Limits for Pair-Interaction Driven Master Equations and Biological Swarm Models

E. Carlen ; P. Degond ; Bernt Wennberg (Institutionen för matematiska vetenskaper, matematik)
Mathematical Models and Methods in Applied Sciences (0218-2025). Vol. 23 (2013), 7, p. 1339-1376.
[Artikel, refereegranskad vetenskaplig]

We consider a class of stochastic processes modeling binary interactions in an N-particle system. Examples of such systems can be found in the modeling of biological swarms. They lead to the definition of a class of master equations that we call pair-interaction driven master equations. In the spatially homogeneous case, we prove a propagation of chaos result for this class of master equations which generalizes Mark Kac's well-known result for the Kac model in kinetic theory. We use this result to study kinetic limits for two biological swarm models. We show that propagation of chaos may be lost at large times and we exhibit an example where the invariant density is not chaotic.

Nyckelord: Master equation, kinetic equations, binary interactions, propagation of chaos, Kac's master, stochastic particle approximations, 3-dimensional rare-gas, mean-field, limit, boltzmann-equation, global validity, continuum-limit, spectral, gap, behavior, vacuum, system

Denna post skapades 2013-05-30. Senast ändrad 2014-09-02.
CPL Pubid: 177678


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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