On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions
 A. V. Bobylev,
 J. A. Carrillo,
 I. M. Gamba
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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, selfsimilar solutions and moment equations. We clarify the conditions under which selfsimilar 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 longwave stability/instability for homogeneous cooling states.
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 Title
 On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions
 Journal

Journal of Statistical Physics
Volume 98, Issue 34 , pp 743773
 Cover Date
 20000201
 DOI
 10.1023/A:1018627625800
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 homogeneous inelastic Boltzmann
 largetime asymptotics
 selfsimilar solutions
 hydrodynamics
 Industry Sectors
 Authors

 A. V. Bobylev ^{(1)}
 J. A. Carrillo ^{(2)} ^{(3)}
 I. M. Gamba ^{(4)}
 Author Affiliations

 1. M. V. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
 2. Department of Mathematics, University of Texas at Austin, 78712, Austin, Texas
 3. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain
 4. Department of Mathematics, University of Texas at Austin, 78712, Austin, Texas, USA