Math. Model. Nat. Phenom.
Volume 11, Number 3, 2016Anomalous diffusion
|Page(s)||63 - 75|
|Published online||21 June 2016|
Feynman-Kac Equations for Random Walks in Disordered Media
Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine 17, General Naumov Str., 03164 Kiev, Ukraine
⋆ Corresponding author. E-mail: firstname.lastname@example.org
The problem of finding the distribution of functional of a trajectory of a particle executing a random walk in a disordered medium containing both traps and obstacles is considered. As a model of disordered medium, the Schirmacher model, a combination of random barriers model and multiple-trapping model, is used. Forward and backward Feynman-Kac equations with the boundary conditions at discontinuity points are formulated. As an example, the distribution of the residence time in a half-space is obtained. It is shown that the anomalous subdiffusion due to traps and that due to obstacles give very different distributions.
Mathematics Subject Classification: 35K57 / 35Q84 / 60G22
Key words: subdiffusion / multiple-trapping / random barriers
© EDP Sciences, 2016
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