{
  "id": "2104.07945",
  "version": "v1",
  "published": "2021-04-16T07:45:10.000Z",
  "updated": "2021-04-16T07:45:10.000Z",
  "title": "Boundary Control for Transport Equations",
  "authors": [
    "Guillaume Bal",
    "Alexandre Jollivet"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper considers two types of boundary control problems for linear transport equations. The first one shows that transport solutions on a subdomain of a domain X can be controlled exactly from incoming boundary conditions for X under appropriate convexity assumptions. This is in contrast with the only approximate control one typically obtains for elliptic equations by an application of a unique continuation property, a property which we prove does not hold for transport equations. We also consider the control of an outgoing solution from incoming conditions, a transport notion similar to the Dirichlet-to-Neumann map for elliptic equations. We show that for well-chosen coefficients in the transport equation, this control may not be possible. In such situations and by (Fredholm) duality, we obtain the existence of non-trivial incoming conditions that are compatible with vanishing outgoing conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-16T07:45:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic equations",
      "appropriate convexity assumptions",
      "linear transport equations",
      "unique continuation property",
      "incoming conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}