{
  "id": "2211.15038",
  "version": "v1",
  "published": "2022-11-28T03:53:33.000Z",
  "updated": "2022-11-28T03:53:33.000Z",
  "title": "Exact controllability for a refined Stochastic Wave Equation",
  "authors": [
    "Zhonghua Liao",
    "Qi Lü"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result, the novelty of this paper is twofold: (1) Our model contains the effects in the drift terms when we put controls directly in the diffusion terms, which is more sensible for practical applications; (2) We provide an explicit description of the waiting time which is sharp in the case of dimension one and is independent of the coefficients of lower terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-28T03:53:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93B05",
      "93B07"
    ],
    "keywords": [
      "refined stochastic wave equation",
      "exact controllability",
      "novel carleman estimate",
      "explicit description",
      "lower terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}