{
  "id": "0902.0987",
  "version": "v2",
  "published": "2009-02-05T21:58:09.000Z",
  "updated": "2009-09-27T11:07:56.000Z",
  "title": "Some asymptotic expansions for a semilinear reaction-diffusion problem in a sector",
  "authors": [
    "R. Bruce Kellogg",
    "Natalia Kopteva"
  ],
  "comment": "18 pages, 1 figure; the figure has been replaced",
  "categories": [
    "math.AP"
  ],
  "abstract": "A semilinear singularly perturbed reaction-diffusion equation with Dirichlet boundary conditions is considered in a convex unbounded sector. The singular perturbation parameter is arbitrarily small, and the \"reduced equation\" may have multiple solutions. A formal asymptotic expansion for a possible solution is constructed that involves boundary and corner layer functions. For this asymptotic expansion, we establish certain inequalities that are used in a subsequent paper to construct sharp sub- and super-solutions and then establish the existence of a solution to a similar nonlinear elliptic problem in a convex polygon.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-27T11:07:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "41A60"
    ],
    "keywords": [
      "semilinear reaction-diffusion problem",
      "similar nonlinear elliptic problem",
      "dirichlet boundary conditions",
      "corner layer functions",
      "semilinear singularly perturbed reaction-diffusion equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.0987K"
    }
  }
}