Analytical Results for the Boltzmann Equation | Zendy

Toepffer C. | Zendy; Cercignani C. | Zendy

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Analytical Results for the Boltzmann Equation

Author(s) -

Toepffer C.,

Cercignani C.

Publication year - 1997

Publication title -

contributions to plasma physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.531

H-Index - 47

eISSN - 1521-3986

pISSN - 0863-1042

DOI - 10.1002/ctpp.2150370217

Subject(s) - boltzmann equation , physics , diffusion equation , momentum (technical analysis) , domain (mathematical analysis) , distribution function , relaxation (psychology) , diffusion , function (biology) , boltzmann constant , constant (computer programming) , statistical physics , mathematical analysis , mathematics , quantum mechanics , programming language , computer science , economics , biology , service (business) , psychology , social psychology , economy , finance , evolutionary biology

The manifold of solutions of the Boltzmann equation in the relaxation time approximation for particles in a constant field is obtained in closed form. The Green's function for the infinite domain and the moments of the probability distribution are calculated explicitly. A generalized drift‐diffusion equation with local temperatures is obtained by matching moments. The Green's function for the finite domain is derived for vanishing equilibrium temperature β → ∞ in a ballistic regime of large momentum gain between collisions.

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