Fractional diffusion and reflective boundary condition

Natalia Krepysheva, Liliana Di Pietro and Marie-Christine Néel

Physica A: Statistical Mechanics and its Applications, 2006, vol. 368, issue 2, 355-361

Abstract: Anomalous diffusive transport arises in a large diversity of disordered media. Stochastic formulations in terms of continuous time random walks (CTRW) with transition probability densities presenting spatial and/or time diverging moments were developed to account for anomalous behaviours. Many CTRWs in infinite media were shown to correspond, on the macroscopic scale, to diffusion equations sometimes involving derivatives of non-integer order. A wide class of CTRWs with symmetric Lévy distribution of jumps and finite mean waiting time leads, in the macroscopic limit, to space-time fractional equations that account for super diffusion and involve an operator, which is non-local in space. Due to non-locality, the boundary condition results in modifying the large-scale model. We are studying here the diffusive limit of CTRWs, generalizing Lévy flights in a semi-infinite medium, limited by a reflective barrier. We obtain space-time fractional diffusion equations that differ from the infinite medium in the kernel of the fractional derivative w.r.t. space.

Keywords: Transport processes; Random media; Continuous time random walks; Integro-differential equations (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:368:y:2006:i:2:p:355-361

DOI: 10.1016/j.physa.2005.11.046

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