{
  "id": "1201.5510",
  "version": "v1",
  "published": "2012-01-26T13:33:17.000Z",
  "updated": "2012-01-26T13:33:17.000Z",
  "title": "Group Actions on Monotone Skew-Product Semiflows with Applications",
  "authors": [
    "Feng Cao",
    "Mats Gyllenberg",
    "Yi Wang"
  ],
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group $G$-action has been considered on a strongly monotone skew-product semiflow. Here we relax the requirement of strong monotonicity of the skew-product semiflows and the compactness of $G$, and establish a theory concerning symmetry or monotonicity properties of uniformly stable 1-cover minimal sets. We then apply this theory to show rotational symmetry of certain stable entire solutions for a class of non-autonomous reaction-diffusion equations on $\\RR^n$, as well as monotonicity of stable travelling waves of some nonlinear diffusion equations in time recurrent structures including almost periodicity and almost automorphy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-26T13:33:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "applications",
      "strongly monotone skew-product semiflow",
      "nonlinear diffusion equations",
      "time recurrent structures",
      "prior work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.5510C"
    }
  }
}