Far Eastern Mathematical Journal

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Anomalous diffusion on interval with reflecting edges

G. Sh. Tsitsiashvili, A. E. Yashin

2003, issue 2, P. 231–241

Abstract

V. V. Uchaikin suggested a mathematical model of an anomalous diffusion in a space. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and etc. In such a model a coordinate of a particle has stable distribution (not normal one). In this article the anomalous diffusion with periodic initial conditions on an interval with reflecting edges is considered. The article is devoted to an investigation of rate convergence of anomalous diffsion to uniform distribution.

Keywords: anomalous diffusion, convergence rate, stable distribution

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References

[1] V. V. Uchaikin, “Multidimensional symmetric anomalous diffusion”, Chemical Physics., 284 (2002), 507–520. [2] N. N. Skvortsova, G. M. Batanov, A. E. Petrov, A. A. Pshenichnikov, K. A. Sarksyan, N. K. Kharchev, “Non-Brownian Particle Motion in Structural Plasma Turbulence”, Proceedings of the XXIII Seminar on Stability for Stochastic Models, Pamplona, Spain, 2003, 88. [3] V. M. Bespalov, G. Sh. Ciciashvili, “O peremeshivanii primesi v vysokoskorostnom gazovom potoke”, Materialy pervogo Rossijsko-korejskogo simpoziuma po matematicheskomu modelirovaniyu, t. 2, IPM DVO RAN, Vladivostok, 1992, 88–96 s. [4] V. S. Vladimirov, Uravneniya matematicheskoj fiziki, Nauka, M., 1967, 436 s. [5] V. Feller, Vvedenie v teoriyu veroyatnostej i ee prilozheniya, t. 2, Mir, M., 1984, 738 s.

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