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Diffusion-approximation for a kinetic equation with perturbed velocity redistribution process. (English) Zbl 1476.35345

Summary: We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the limit we obtain is a parabolic stochastic partial differential equation on the macroscopic parameter, the density here.

MSC:

35R60 PDEs with randomness, stochastic partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
35Q20 Boltzmann equations
35Q49 Transport equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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