{
  "id": "2009.13035",
  "version": "v1",
  "published": "2020-09-28T03:03:44.000Z",
  "updated": "2020-09-28T03:03:44.000Z",
  "title": "Patterns with prescribed numbers of critical points on topological tori",
  "authors": [
    "Putri Zahra Kamalia",
    "Shigeru Sakaguchi"
  ],
  "comment": "16 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence of critical points of stable stationary solutions to reaction-diffusion problems on topological tori. Stable nonconstant stationary solutions are often called patterns. We construct topological tori and patterns with prescribed numbers of critical points whose locations are explicit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-28T03:03:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B35",
      "35K57",
      "35K58",
      "35J61",
      "35P15",
      "35K15",
      "35K20",
      "35B20",
      "58J05"
    ],
    "keywords": [
      "critical points",
      "prescribed numbers",
      "stable nonconstant stationary solutions",
      "stable stationary solutions",
      "reaction-diffusion problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}