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- W2962876945 abstract "We consider the spatially homogeneous Boltzmann equation for hard potentials with angular cutoff. This equation has a unique conservative weak solution $ (f_t)_{tgeq 0} $, once the initial condition $ f_0 $ with finite mass and energy is fixed. Taking advantage of the energy conservation, we propose a recursive algorithm that produces a $ (0,infty)times {mathbb{R}}^3 $ random variable $ (M_t,V_t) $ such that $ mathbb{E}[M_t {bf 1}_{{V_t in cdot}}] = f_t $. We also write down a series expansion of $ f_t $. Although both the algorithm and the series expansion might be theoretically interesting in that they explicitly express $ f_t $ in terms of $ f_0 $, we believe that the algorithm is not very efficient in practice and that the series expansion is rather intractable. This is a tedious extension to non-Maxwellian molecules of Wild's sum [18] and of its interpretation by McKean [10,11]." @default.
- W2962876945 created "2019-07-30" @default.
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- W2962876945 date "2019-01-01" @default.
- W2962876945 modified "2023-09-27" @default.
- W2962876945 title "A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff" @default.
- W2962876945 doi "https://doi.org/10.3934/krm.2019020" @default.
- W2962876945 hasPublicationYear "2019" @default.
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