{
  "id": "1210.6419",
  "version": "v1",
  "published": "2012-10-24T01:32:58.000Z",
  "updated": "2012-10-24T01:32:58.000Z",
  "title": "Global continuation of monotone wavefronts",
  "authors": [
    "Adrian Gomez",
    "Sergei Trofimchuk"
  ],
  "comment": "21 pages, 3 figures, submitted",
  "journal": "Journal of the London Mathematical Society, (2) 89 (2014) 47-68",
  "doi": "10.1112/jlms/jdt050",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "In this paper, we answer the question about the criteria of existence of monotone travelling fronts $u = \\phi(\\nu \\cdot x+ct), \\phi(-\\infty) =0, \\phi(+\\infty) = \\kappa,$ for the monostable (and, in general, non-quasi-monotone) delayed reaction-diffusion equations $u_t(t,x) - \\Delta u(t,x) = f(u(t,x), u(t-h,x)).$ $C^{1,\\gamma}$-smooth $f$ is supposed to satisfy $f(0,0) = f(\\kappa,\\kappa) =0$ together with other monostability restrictions. Our theory covers the two most important cases: Mackey-Glass type diffusive equations and KPP-Fisher type equations. The proofs are based on a variant of Hale-Lin functional-analytic approach to the heteroclinic solutions where Lyapunov-Schmidt reduction is realized in a `mobile' weighted space of $C^2$-smooth functions. This method requires a detailed analysis of a family of associated linear differential Fredholm operators: at this stage, the discrete Lyapunov functionals by Mallet-Paret and Sell are used in an essential way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-24T01:32:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K12",
      "35K57",
      "92D25"
    ],
    "keywords": [
      "global continuation",
      "monotone wavefronts",
      "associated linear differential fredholm operators",
      "discrete lyapunov functionals",
      "mackey-glass type diffusive equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6419G"
    }
  }
}