{
  "id": "2104.01597",
  "version": "v1",
  "published": "2021-04-04T12:24:28.000Z",
  "updated": "2021-04-04T12:24:28.000Z",
  "title": "Initial boundary value problem of a class of pseudo-parabolic Kirchhoff equations with logarithmic nonlinearity",
  "authors": [
    "Qiuting Zhao"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the initial boundary value problem for a pseudo-parabolic Kirchhoff equation with logarithmic nonlinearity. We use the potential well method to give a threshold result of global existence and finite-time blow-up for the weak solutions with initial energy $J(u_0)\\leq d$. When the initial energy $J(u_0)>d$, we find another criterion for the vanishing solution and blow-up solution. We also get the exponential decay rate of the global solution and life span of the blow-up solution. Meanwhile, we study the corresponding stationary problem and establish a convergence relationship between its ground state solution and the global solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-04T12:24:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial boundary value problem",
      "pseudo-parabolic kirchhoff equation",
      "logarithmic nonlinearity",
      "global solution",
      "blow-up solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}