Journal of Statistical Physics

, Volume 98, Issue 3–4, pp 743–773

On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions

  • A. V. Bobylev
  • J. A. Carrillo
  • I. M. Gamba
Article

Abstract

We investigate a Boltzmann equation for inelastic scattering in which the relative velocity in the collision frequency is approximated by the thermal speed. The inelasticity is given by a velocity variable restitution coefficient. This equation is the analog to the Boltzmann classical equation for Maxwellian molecules. We study the homogeneous regime using Fourier analysis methods. We analyze the existence and uniqueness questions, the linearized operator around the Dirac delta function, self-similar solutions and moment equations. We clarify the conditions under which self-similar solutions describe the asymptotic behavior of the homogeneous equation. We obtain formally a hydrodynamic description for near elastic particles under the assumption of constant and variable restitution coefficient. We describe the linear long-wave stability/instability for homogeneous cooling states.

homogeneous inelastic Boltzmann large-time asymptotics self-similar solutions hydrodynamics 

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • A. V. Bobylev
    • 1
  • J. A. Carrillo
    • 2
    • 3
  • I. M. Gamba
    • 4
  1. 1.M. V. Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.Department of MathematicsUniversity of Texas at AustinAustin
  3. 3.Departamento de Matemática Aplicada, Facultad de CienciasUniversidad de GranadaGranadaSpain
  4. 4.Department of MathematicsUniversity of Texas at AustinAustinUSA

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