 99128 A. V. Bobylev, J. A. Carrillo, I. Gamba
 On some properties of kinetic and hydrodynamic equations for inelastic interaction
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Apr 23, 99

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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 analogous to the Boltzmann classical equation for Maxwellian molecules. We study the homogeneous regime using Fourier analysis methods. We
analyze the existence and uniqueness questions, linearized operator around Dirac delta function,
selfsimilar solutions and moment equations. We clarify the conditions under which the selfsimilar
solutions describe the large time 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 the homogeneous cooling
states.
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