{
  "id": "2007.11989",
  "version": "v1",
  "published": "2020-07-23T13:02:16.000Z",
  "updated": "2020-07-23T13:02:16.000Z",
  "title": "Existence of a global weak solution for a reaction-diffusion problem with membrane conditions",
  "authors": [
    "Giorgia Ciavolella",
    "Benoît Perthame"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Several problems, issued from physics or biology, lead to parabolic equations set in two sub-domains separated by a membrane. The corresponding boundary conditions are compatible with mass conservation and are called the Kedem-Katchalsky conditions. In these models, written as reaction-diffusion systems, the reaction terms have a quadratic behaviour. We adapt the $L^1$ theory developed by M. Pierre and collaborators to these boundary conditions and prove the existence of weak solutions when the initial data has $L^1$ regularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-23T13:02:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K57",
      "35D30",
      "35Q92"
    ],
    "keywords": [
      "global weak solution",
      "reaction-diffusion problem",
      "membrane conditions",
      "parabolic equations set",
      "reaction terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}