Abstract
A locally nonequilibrium model of superdiffusion is proposed that is based on the partition of the set of diffusing particles into groups according to the flight length of these particles. The process of diffusion is described in terms of partial concentrations of particles belonging to different groups. As special limit cases, the model yields equations with fractional time derivative and the so-called porous medium equation. The basic equations of the model are Markov equations; therefore, they easily include reaction terms. The model can be applied to describing the types of diffusion in which the diffusing particles are in free flight most of the time.
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Original Russian Text © V.P. Shkilev, 2008, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 134, No. 5, pp. 1040–1047.