{
  "id": "1505.03280",
  "version": "v1",
  "published": "2015-05-13T09:07:16.000Z",
  "updated": "2015-05-13T09:07:16.000Z",
  "title": "Existence of solutions for a model of microwave heating",
  "authors": [
    "Pierluigi Colli",
    "Luca Scarpa"
  ],
  "comment": "Key words and phrases: microwave heating, circuit model, evolutionary system of partial differential equations, weak solution, global existence",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with a system of differential equations related to a circuit model for microwave heating, complemented by suitable initial and boundary conditions. A RCL circuit with a thermistor is representing the microwave heating process with temperature-induced modulations on the electric field. The unknowns of the PDE system are the absolute temperature in the body, the voltage across the capacitor and the electrostatic potential. Using techniques based on monotonicity arguments and sharp estimates, we can prove the existence of a weak solution to the initial-boundary value problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-13T09:07:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35G61",
      "34A10",
      "35D30",
      "35Q79"
    ],
    "keywords": [
      "initial-boundary value problem",
      "circuit model",
      "boundary conditions",
      "rcl circuit",
      "microwave heating process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150503280C"
    }
  }
}