Open AccessThe uniformly heated inelastic Boltzmann equation in Fourier space
Author(s) -
Ralf Kirsch,
Sergej Rjasanow
Publication year - 2010
Publication title -
kinetic and related models
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.987
H-Index - 28
eISSN - 1937-5093
pISSN - 1937-5077
DOI - 10.3934/krm.2010.3.445
Subject(s) - fourier transform , boltzmann equation , constant (computer programming) , a priori and a posteriori , mathematical analysis , extension (predicate logic) , variable (mathematics) , physics , space (punctuation) , integral equation , kernel (algebra) , hard spheres , mathematics , spheres , thermodynamics , pure mathematics , philosophy , linguistics , epistemology , astronomy , computer science , programming language
In this article, we present an alternative formulation of the Boltzmann equation for diffusively driven granular media. The equation is considered with minimal a priori assumptions, i.e. in weak form in the sense of tempered distributions. Using shifted test functions and the Fourier transform, it is seen that the transformed problem contains only a threefold integral. For constant restitution coefficients and the variable hard spheres model, explicit expressions of the integral kernel in the transformed collision operator are obtained. The version of the equation derived here is a true extension of the elastic case. Some well-known results for Maxwell molecules with inelastic interactions are recovered