{
  "id": "1810.00975",
  "version": "v1",
  "published": "2018-10-01T20:53:21.000Z",
  "updated": "2018-10-01T20:53:21.000Z",
  "title": "Global dynamics for a class of reaction-diffusion equations with distributed delay and Neumann condition",
  "authors": [
    "Tarik Mohammed Touaoula"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we investigate a class of non-monotone reaction-diffusion equations with distributed delay and a homogenous boundary Neumann condition, which have a positive steady state. The main concern is the global attractivity of the unique positive steady state. To achieve this, we use an argument of a sub and super-solution combined with fluctuation method. We also give a condition for which the exponential stability of the positive steady state is reached. As an example, we apply our results to diffusive Nicholson blowflies and diffusive Mackey-Glass equation with distributed delay. We point out that we obtain some new results on exponential stability of the positive steady state for these cited models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-01T20:53:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distributed delay",
      "global dynamics",
      "exponential stability",
      "unique positive steady state",
      "homogenous boundary neumann condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}