{
  "id": "1003.2275",
  "version": "v1",
  "published": "2010-03-11T08:36:18.000Z",
  "updated": "2010-03-11T08:36:18.000Z",
  "title": "Layer Potential Techniques for the Narrow Escape Problem",
  "authors": [
    "Habib Ammari",
    "Kostis Kalimeris",
    "Hyeonbae Kang",
    "Hyundae Lee"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The narrow escape problem consists of deriving the asymptotic expansion of the solution of a drift-diffusion equation with the Dirichlet boundary condition on a small absorbing part of the boundary and the Neumann boundary condition on the remaining reflecting boundaries. Using layer potential techniques, we rigorously find high-order asymptotic expansions of such solutions. We explicitly show the nonlinear interaction of many small absorbing targets. Based on the asymptotic theory for eigenvalue problems developed in \\cite{book}, we also construct high-order asymptotic formulas for eigenvalues of the Laplace and the drifted Laplace operators for mixed boundary conditions on large and small pieces of the boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-11T08:36:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "92B05"
    ],
    "keywords": [
      "layer potential techniques",
      "asymptotic expansion",
      "construct high-order asymptotic formulas",
      "narrow escape problem consists",
      "neumann boundary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.2275A"
    }
  }
}