{
  "id": "2501.03815",
  "version": "v1",
  "published": "2025-01-07T14:27:57.000Z",
  "updated": "2025-01-07T14:27:57.000Z",
  "title": "Curved fronts of bistable reaction-diffusion equations in spatially periodic media: $N\\ge 2$",
  "authors": [
    "Hongjun Guo",
    "Haijian Wang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with curved fronts of bistable reaction-diffusion equations in spatially periodic media for dimensions $N\\geq 2$. The curved fronts concerned are transition fronts connecting $0$ and $1$. Under a priori assumption that there exist moving pulsating fronts in every direction, we show the existence of polytope-like curved fronts with $0$-zone being a polytope and $1$-zone being the complementary set. By reversing some conditions, we also show the existence of curved fronts with reversed $0$-zone and $1$-zone. Furthermore, the curved fronts constructed by us are proved to be unique and asymptotic stable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-07T14:27:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "curved fronts",
      "bistable reaction-diffusion equations",
      "spatially periodic media",
      "transition fronts",
      "priori assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}