{
  "id": "1608.02188",
  "version": "v1",
  "published": "2016-08-07T06:47:05.000Z",
  "updated": "2016-08-07T06:47:05.000Z",
  "title": "Convergence of the Finite Difference Scheme for a General Class of Multi-phase Obstacle-like problems",
  "authors": [
    "Avetik Arakelyan"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this work we prove convergence of the finite difference scheme for equations of stationary states of a general class of the spatial segregation of reaction-diffusion systems with $m\\geq 2$ components. More precisely, we show that the numerical solution $u_h^l$, given by the difference scheme, converges to the $l^{th}$ component $u_l,$ when the mesh size $h$ tends to zero, provided $u_l\\in C^2(\\Omega),$ for every $l=1,2,\\dots,m.$ In particular, our proof provides convergence of a difference scheme for the multi-phase obstacle problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-07T06:47:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35",
      "65N06",
      "65N22",
      "92D25"
    ],
    "keywords": [
      "finite difference scheme",
      "multi-phase obstacle-like problems",
      "general class",
      "convergence",
      "multi-phase obstacle problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}