Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-12-21
Physics
Condensed Matter
Statistical Mechanics
15 pages, 4 figures. Accepted in J. Statistical Physics
Scientific paper
This paper deals with solutions of the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell models for large times and for large velocities, and the nonuniform convergence to these limits. We demonstrate how the velocity distribution approaches in the scaling limit to a similarity solution with a power law tail for general classes of initial conditions and derive a transcendental equation from which the exponents in the tails can be calculated. Moreover on the basis of the available analytic and numerical results for inelastic hard spheres and inelastic Maxwell models we formulate a conjecture on the approach of the velocity distribution function to a scaling form.
Brito Ricardo
Ernst Matthieu H.
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