{
  "id": "2305.00525",
  "version": "v1",
  "published": "2023-04-30T16:51:05.000Z",
  "updated": "2023-04-30T16:51:05.000Z",
  "title": "Stability for backward problems in time for degenerate parabolic equations",
  "authors": [
    "Piermarco Cannarsa",
    "Masahiro Yamamoto"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "For solution $u(x,t)$ to degenearte parabolic equations in a bounded domain $\\Omega$ with homogenous boundary condition, we consider backward problems in time: determine $u(\\cdot,t_0)$ in $\\Omega$ by $u(\\cdot,T)$, where $t$ is the time variable and $0\\le t_0 < T$. Our main results are conditional stability under boundedness assumptions on $u(\\cdot,0)$. The proof is based on a weighted $L^2$-estimate of $u$ whose weight depends only on $t$, which is an inequality of Carleman's type. Moreover our method is applied to semilinear degenerate parabolic equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-30T16:51:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "backward problems",
      "semilinear degenerate parabolic equations",
      "degenearte parabolic equations",
      "homogenous boundary condition",
      "main results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}