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Stationary states for the noncutoff Kac equation with a Gaussian thermostat. (English) Zbl 1171.82311
Summary: We study the stationary states of a Kac equation with a Gaussian thermostat in the case of a noncutoff cross section. We investigate the existence, smoothness and uniqueness of the stationary states. The theoretical results are illustrated by some numerical simulations.

MSC:
82B40Kinetic theory of gases (equilibrium statistical mechanics)
45J05Integro-ordinary differential equations
42A38Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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