{
  "id": "1611.07081",
  "version": "v1",
  "published": "2016-11-21T22:23:33.000Z",
  "updated": "2016-11-21T22:23:33.000Z",
  "title": "Subdiffusion--absorption process in a system consisting of two different media",
  "authors": [
    "Tadeusz Kosztołowicz"
  ],
  "comment": "7 pages, 6 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Subdiffusion with reaction $A+B\\rightarrow B$ is considered in a system which consists of two homogeneous media joined together; the $A$ particles are mobile whereas $B$ are static. Subdiffusion and reaction parameters, which are assumed to be independent of time and space variable, can be different in both media. Particles $A$ move freely across the border between the media. In each part of the system the process is described by the subdiffusion--reaction equations with fractional time derivative. By means of the method presented in this paper we derive both the fundamental solutions (the Green's functions) $P(x,t)$ to the subdiffusion--reaction equations and the boundary conditions at the border between the media. One of the conditions demands the continuity of a flux and the other one contains the Riemann--Liouville fractional time derivatives $\\partial^{\\alpha_1}P(0^+,t)/\\partial t^{\\alpha_1}=(D_1/D_2)\\partial^{\\alpha_2}P(0^-,t)/\\partial t^{\\alpha_2}$, where the subdiffusion parameters $\\alpha_1$, $D_1$ and $\\alpha_2$, $D_2$ are defined in the regions $x<0$ and $x>0$, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-21T22:23:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "subdiffusion-absorption process",
      "system consisting",
      "riemann-liouville fractional time derivatives",
      "subdiffusion-reaction equations",
      "reaction parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}