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Zbl 1060.82518
Frank, T.D.; Daffertshofer, A.
Exact time-dependent solutions of the Rényi Fokker-Planck equation and the Fokker-Planck equations related to the entropies proposed by Sharma and Mittal. (English)
[J] Physica A 285, No. 3-4, 351-366 (2000). ISSN 0378-4371

Summary: Exact time-dependent solutions representing generalized one-dimensional Ornstein-Uhlenbeck processes are derived from nonlinear Fokker-Planck equations and the corresponding diffusion processes are studied. The corresponding systems are related to the Rényi entropy and entropies proposed by Sharma and Mittal. In the former case normal diffusion is found with a diffusion rate depending on the order of the Rényi entropy. In the latter case we find anomalous diffusion processes.

MSC 2000:: *82C31 Stochastic methods in time-dependent statistical mechanics
82C70 Transport processes
94A17 Measures of information
35Q99 PDE of mathematical physics and other areas
35K55 Nonlinear parabolic equations

Keywords: exact time-dependent solutions; Renyi-Fokker-Planck equation; Fokker-Planck equation; Sharma-Mittal entropy; 1D-Ornstein-Uhlenbeck processes; Renyi entropy; anomalous diffusion; diffusion rate

Cited in: Zbl 1136.94315

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