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2010, Volume 3, Issue 3: 445-456. Doi: 10.3934/krm.2010.3.445
This issue Previous Article Asymptotic behaviour of reversible chemical reaction-diffusion equations Next Article Strengthened convergence of marginals to the cubic nonlinear Schrödinger equation

The uniformly heated inelastic Boltzmann equation in Fourier space

  • 1.

    Department of Flow and Material Simulation, Fraunhofer ITWM, Fraunhofer-Platz 1, D-67663 Kaiserslautern

  • 2.

    Department of Mathematics, Saarland University, P.O. Box 15 11 50, D-66041 Saarbrücken

Received:  December 31, 2009
Revised:  April 30, 2010
Published:  August 2010
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: 82C40, 76P05.

    Citation:
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