Benedetto, D.; Caglioti, E.; Carrillo, J. A.; Pulvirenti, M. A non-Maxwellian steady distribution for one-dimensional granular media. (English) Zbl 0921.60057 J. Stat. Phys. 91, No. 5-6, 979-990 (1998). 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. Cited in 66 Documents 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 Keywords:granular media; inelastic collisions; kinetic equations; Fokker-Planck PDFBibTeX XMLCite \textit{D. Benedetto} et al., J. Stat. Phys. 91, No. 5--6, 979--990 (1998; Zbl 0921.60057) Full Text: DOI