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arXiv · 1812.02857

Finite-velocity diffusion on a comb

Trifce Sandev·Alexander Iomin
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Abstract

A Cattaneo equation for a comb structure is considered. We present a rigorous analysis of the obtained fractional diffusion equation, and corresponding solutions for the probability distribution function are obtained in the form of the Fox $H$-function and its infinite series. The mean square displacement along the backbone is obtained as well in terms of the infinite series of the Fox $H$-function. The obtained solutions describe the transition from normal diffusion to subdiffusion, which results from the comb geometry.

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Trifce Sandev, Alexander Iomin. 2018-12-07. Finite-velocity diffusion on a comb. https://doi.org/10.1209/0295-5075%2F124%2F20005

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