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We present an alternative formulation of the spatially homogenous Boltzmann equation. Rewriting the weak form of the equation with shifted test functions and using Fourier techniques, it turns out that the transformed problem contains only a three-fold integral for most general collision kernels.
Explicit formulas for the transformed collision kernel are presented in the case of VHS models for hard and soft potentials. For isotropic Maxwellian molecules, a classical result by Bobylev is recovered, too. Furthermore, the numerical treatment of the Boltzmann equation using this alternative formulation is discussed.
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