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A non-Maxwellian steady distribution for one-dimensional granular media. (English) Zbl 0921.60057
Summary: We consider a nonlinear Fokker-Planck equation for a one-dimensional granular medium. This is a kinetic approximation of a system of nearly elastic particles in a thermal bath. We prove that homogeneous solutions tend asymptotically in time toward a unique non-Maxwellian stationary distribution.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
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