{
  "id": "1409.4679",
  "version": "v1",
  "published": "2014-09-16T15:47:37.000Z",
  "updated": "2014-09-16T15:47:37.000Z",
  "title": "On a model of a population with variable motility",
  "authors": [
    "Olga Turanova"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and long-range) behavior of the population. We perform a certain rescaling and prove that solutions of the rescaled problem converge locally uniformly to zero in a certain region and stay positive (in some sense) in another region. These regions are determined by two viscosity solutions of a related Hamilton-Jacobi equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-16T15:47:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "variable motility",
      "population",
      "problem converge",
      "nonlocal reaction term",
      "global supremum bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.4679T"
    }
  }
}