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KRM

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.

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