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Anomalous diffusion, solutions, and first passage time: Influence of diffusion coefficient

Kwok Sau Fa, Ervin Kaminski Lenzi

Abstract

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the usual diffusion equation. We consider a space- and time-dependent diffusion coefficient and the presence of absorbing boundaries. We obtain analytical results for the probability distribution and the first passage time distribution for finite and semi-infinite intervals. In addition, we compare our results for the first passage time distribution with the one obtained by the usual diffusion equation with constant diffusion coefficient.

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Key concepts: Diffusion, Anomalous diffusion, Effective diffusion coefficient, Diffusion equation, First-hitting-time model, Fick's laws of diffusion, Distribution (mathematics), Photon transport in biological tissue