{
  "id": "1803.06757",
  "version": "v1",
  "published": "2018-03-18T22:12:51.000Z",
  "updated": "2018-03-18T22:12:51.000Z",
  "title": "On stabilization of solutions of higher order evolution inequalities",
  "authors": [
    "A. A. Kon'kov",
    "A. E. Shishkov"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain sharp conditions guaranteeing that every non-negative weak solution of the inequality $$ \\sum_{|\\alpha| = m} \\partial^\\alpha a_\\alpha (x, t, u) - u_t \\ge f (x, t) g (u) \\quad \\mbox{in} {\\mathbb R}_+^{n+1} = {\\mathbb R}^n \\times (0, \\infty), \\quad m,n \\ge 1, $$ stabilizes to zero as $t \\to \\infty$. These conditions generalize the well-known Keller-Osserman condition on the grows of the function $g$ at infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-18T22:12:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K25",
      "35K55",
      "35K65",
      "35B09",
      "35B40"
    ],
    "keywords": [
      "inequality",
      "higher order evolution inequalities",
      "stabilization",
      "well-known keller-osserman condition",
      "non-negative weak solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}