{
  "id": "1810.09664",
  "version": "v1",
  "published": "2018-10-21T16:53:37.000Z",
  "updated": "2018-10-21T16:53:37.000Z",
  "title": "A note on a weakly coupled system of semi-linear visco-elastic damped $σ$-evolution models with different power nonlinearities and different $σ$ values",
  "authors": [
    "Tuan Anh Dao"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1809.06744",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we prove the global (in time) existence of small data solutions from energy spaces basing on $L^q$ spaces, with $q \\in (1,\\infty)$, to the Cauchy problems for a weakly coupled system of semi-linear visco-elastic damped $\\sigma$-evolution models. Here we consider different power nonlinearities and different $\\sigma$ values in the comparison between two single equations. To do this, we use $(L^m \\cap L^q)- L^q$ and $L^q- L^q$ estimates, i.e., by mixing additional $L^m$ regularity for the data on the basis of $L^q- L^q$ estimates for solutions, with $m \\in [1,q)$, to the corresponding linear Cauchy problems. In addition, allowing loss of decay and the flexible choice of parameters $\\sigma$, $m$ and $q$ bring some benefits to relax the restrictions to the admissible exponents $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-21T16:53:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L30",
      "35L56",
      "35R11"
    ],
    "keywords": [
      "weakly coupled system",
      "evolution models",
      "power nonlinearities",
      "semi-linear visco-elastic",
      "corresponding linear cauchy problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}