{
  "id": "2004.10460",
  "version": "v1",
  "published": "2020-04-22T09:26:29.000Z",
  "updated": "2020-04-22T09:26:29.000Z",
  "title": "Approximate controllability of a non-autonomus evolution equation in Banach spaces",
  "authors": [
    "K. Ravikumar",
    "M. T. Mohan",
    "A. Anguraj"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we consider a non-autonomus nonlinear evolution equation in separable, reflexive Banach spaces. First, we consider a linear problem and establish the approximate controllability results by finding a feedback control with the help of an optimal control problem. We then establish the approximate controllability results for a semilinear differential equation in Banach spaces using the theory of linear evolution systems, properties of resolvent operator and Schauder's fixed point theorem. Finally, we provide an example of a non-autonomous, nonlinear diffusion equation in Banach spaces to validate the results we obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-22T09:26:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K06",
      "34A12",
      "37L05",
      "93B05"
    ],
    "keywords": [
      "banach spaces",
      "non-autonomus evolution equation",
      "approximate controllability results",
      "non-autonomus nonlinear evolution equation",
      "optimal control problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}