Summary
This paper presents a study of the relation between the Boltzmann equation and a nonlinear integral evolution equation, sometimes called the Boltzmann equation in the scattering kernel formulation. In particular, we investigate under what conditions conservation laws analogous to those holding for the Boltzmann equation hold for the scattering kernel form as well.
Riassunto
In questo lavoro si studiano le relazioni tra l–equazione di Boltzmann e un–equazione di evoluzione integrale non lineare, talvolta denominata equazione di Boltzmann nella forma dello scattering kernel. In particolare si studia sotto quali condizioni delle leggi di conservazione analoghe a quelle valevoli per l–equazione di Boltzmann valgono pure per la forma dello scattering kernel.
Резюме
В этой статье исследуется связь между уравнением Больцмана и нелинейными уравнением эволюции, которое иногда называют уравнением Больцмана в формулировке с ядром рассеяния. В частности, мы исследуем, при каких условиях законы сохранения, аналогичные законам сохранения для уравнения Больцмана, справедливы также для случая формулировки с ядром рассеяния.
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Cercignani, C., Sgarra, C. & Lampis, M. On the relation between the scattering kernel and the standard formulation of the Boltzmann equation. Nuov Cim B 101, 523–531 (1988). https://doi.org/10.1007/BF02748956
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DOI: https://doi.org/10.1007/BF02748956