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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) Zbl 1060.82518
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:
82C31Stochastic methods in time-dependent statistical mechanics
82C70Transport processes (time-dependent statistical mechanics)
94A17Measures of information, entropy
35Q99PDE of mathematical physics and other areas
35K55Nonlinear parabolic equations