{
  "id": "2004.01226",
  "version": "v1",
  "published": "2020-04-02T19:04:46.000Z",
  "updated": "2020-04-02T19:04:46.000Z",
  "title": "Exact thresholds in the dynamics of cold plasma with electron-ion collisions",
  "authors": [
    "Olga Rozanova",
    "Eugeniy Chizhonkov",
    "Maria Delova"
  ],
  "comment": "14 pages, 6 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "physics.plasm-ph"
  ],
  "abstract": "We consider a quasilinear system of hyperbolic equations that describes plane one-dimensional non-relativistic oscillations of electrons in a cold plasma with allowance for electron-ion collisions. Accounting for collisions leads to the appearance of a term analogous to dry friction in a mechanical system, leading to a decrease in the total energy. We obtain a criterion for the existence of a global in time smooth solution to the Cauchy problem. It allows to accurately separate the initial data into two classes: one corresponds to a globally in time smooth solutions, and the other leads to a finite-time blowup. The influence of electron collision frequency $ \\nu $ on the solution is investigated. It is shown that there is a threshold value, after exceeding which the regime of damped oscillations is replaced by the regime of monotonic damping. The set of initial data corresponding to a globally in time smooth solution of the Cauchy problem expands with increasing $ \\nu $, however, at an arbitrarily large value there are smooth initial data for which the solution forms a singularity in a finite time, and this time tends to zero as $ \\nu $ tends to infinity. The character of the emerging singularities is illustrated by numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-02T19:04:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L60",
      "35L67",
      "78A25"
    ],
    "keywords": [
      "cold plasma",
      "electron-ion collisions",
      "time smooth solution",
      "exact thresholds",
      "initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}