The grazing collision limit for the Boltzmann–Lorentz model
Résumé
The Lorentz operators are derived from either Boltzmann or Fokker–Planck collisions operators when considering a mixture of species with disparate masses [8]. The Fokker–Planck operator is the so called “grazing collision limit” of the Boltzmann operator as proved in [1,12,7]. In our simpler case, we improve the results by proving uniform in time convergence and by controling the speed of the trend to equilibrium. The results are based on a spectral analysis of the operators which share the same basis of eigenfunctions.
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