Subdiffusion with External Time Modulation

R. Wojnar IPPT PAN,Świętokrzyska 21, 00-049 Warszawa, Poland

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Received: 22 11 2007;

A subdiffusion process, similar to a Zeldovich-Kompaneets heat conduction process, is defined by a nonlinear diffusion equation in which the diffusion coefficient takes the form D=a(t)f n, where a=a(t) is an external time modulation, n is a positive constant, and f=f(x, t) is a solution to the nonlinear diffusive equation. It is shown that a Zeldovich-Kompaneets solution satisfies the subdiffusion equation if a=a(t) is replaced by the mean value of a. Also, a solution to the subdiffusion equation is constructed that may be useful in description of biological, social, and financial processes.

DOI: 10.12693/APhysPolA.114.607 PACS numbers: 05.40.Jc, 05.70.Ln, 82.39.Rt, 87.18.Hf, 89.65.Gh, 89.65.Lm