Ansatz solutions to the Cauchy initial value problem of the nonlinear particle transport theory

Authors:
V. C. Boffi
Affiliations:
Dipartimento di Meccanica e Aeronautica Università "La Sapienza" via Eudossiana 18 i-00184 Roma Italy
Venue:
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Year:
2002

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Abstract

Explicit analytical solutions to a nonlinear spatially homogeneous model Boltzmann equation are presented for a physical situation of reference, characterized by constant collision frequencies and scattering probability distributions depending only on the velocity after collision. It is shown that these rigorous solutions can, alternatively, be expressed in terms of the incomplete beta-function, the Gaussian hypergeometric function or the Fox H-function.