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The Kac equation with a thermostatted force field. (English) Zbl 1134.82041
Summary: We consider the Kac equation with a thermostatted force field and prove the existence of a global in time solution that converges weakly to a stationary state. As there is no an obvious candidate for the entropy functional, in this case, the convergence result is obtained via Fourier transform techniques.

MSC:
82C40Kinetic theory of gases (time-dependent statistical mechanics)
82C31Stochastic methods in time-dependent statistical mechanics
76P05Rarefied gas flows, Boltzmann equation
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References:
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