{
  "id": "2411.12267",
  "version": "v1",
  "published": "2024-11-19T06:38:48.000Z",
  "updated": "2024-11-19T06:38:48.000Z",
  "title": "Cost of controllability of the Burgers equation linearized at a steady shock in the vanishing viscosity limit",
  "authors": [
    "Vincent Laheurte"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the one-dimensional Burgers equation linearized at a stationary shock, and investigate its null-controllability cost with a control at the left endpoint. We give an upper and a lower bound on the control time required for this cost to remain bounded in the vanishing viscosity limit, as well as a rough description of an admissible control. The proof relies on complex analysis and adapts methods previously used to tackle the same issue with a constant transport term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-19T06:38:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93C20"
    ],
    "keywords": [
      "vanishing viscosity limit",
      "steady shock",
      "constant transport term",
      "one-dimensional burgers equation",
      "proof relies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}