{
  "id": "2011.00599",
  "version": "v1",
  "published": "2020-11-01T18:56:45.000Z",
  "updated": "2020-11-01T18:56:45.000Z",
  "title": "On large time behavior of solutions of higher order evolution inequalities with fast diffusion",
  "authors": [
    "A. A. Kon'kov",
    "A. E. Shishkov"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain stabilization conditions and large time estimates for weak solutions of the inequality $$ \\sum_{|\\alpha| = m} \\partial^\\alpha a_\\alpha (x, t, u) - u_t \\ge f (x, t) g (u) \\quad \\mbox{in } \\Omega \\times (0, \\infty), $$ where $\\Omega$ is a non-empty open subset of ${\\mathbb R}^n$, $m, n \\ge 1$, and $a_\\alpha$ are Caratheodory functions such that $$ |a_\\alpha (x, t, \\zeta)| \\le A \\zeta^p, \\quad |\\alpha| = m, $$ with some constants $A > 0$ and $0 < p < 1$ for almost all $(x, t) \\in \\Omega \\times (0, \\infty)$ and for all $\\zeta \\in [0, \\infty)$. For solutions of homogeneous differential inequalities, we give an exact universal upper bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-01T18:56:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35G20",
      "35K25",
      "35K55",
      "35K65"
    ],
    "keywords": [
      "higher order evolution inequalities",
      "large time behavior",
      "fast diffusion",
      "inequality",
      "exact universal upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}