{
  "id": "1702.02129",
  "version": "v1",
  "published": "2017-02-07T18:28:51.000Z",
  "updated": "2017-02-07T18:28:51.000Z",
  "title": "On stabilization of solutions of nonlinear parabolic equations with a gradient term",
  "authors": [
    "Andrej A. Kon'kov"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "For parabolic equations of the form $$ \\frac{\\partial u}{\\partial t} - \\sum_{i,j=1}^n a_{ij} (x, u) \\frac{\\partial^2 u}{\\partial x_i \\partial x_j} + f (x, u, D u) = 0 \\quad \\mbox{in } {\\mathbb R}_+^{n+1}, $$ where ${\\mathbb R}_+^{n+1} = {\\mathbb R}^n \\times (0, \\infty)$, $n \\ge 1$, $D = (\\partial / \\partial x_1, \\ldots, \\partial / \\partial x_n)$ is the gradient operator, and $f$ is some function, we obtain conditions guaranteeing that every solution tends to zero as $t \\to \\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-07T18:28:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear parabolic equations",
      "gradient term",
      "stabilization",
      "gradient operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}