{
  "id": "2305.03397",
  "version": "v1",
  "published": "2023-05-05T09:40:59.000Z",
  "updated": "2023-05-05T09:40:59.000Z",
  "title": "Reaction-diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions",
  "authors": [
    "T. G. de Jong",
    "G. Prokert",
    "A. E. Sterk"
  ],
  "categories": [
    "math.AP",
    "q-bio.CB"
  ],
  "abstract": "We investigate a nonlinear parabolic reaction-diffusion equation describing the oxygen concentration in encapsulated pancreatic cells with a general core-shell geometry. This geometry introduces a discontinuous diffusion coefficient as the material properties of the core and shell differ. We apply monotone operator theory to show well-posedness of the problem in the strong form. Furthermore, the stationary solutions are unique and asymptotically stable. These results rely on the gradient structure of the underlying PDE.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-05T09:40:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92C50",
      "35K55",
      "34K20"
    ],
    "keywords": [
      "stationary solutions",
      "reaction-diffusion transport",
      "well-posedness",
      "nonlinear parabolic reaction-diffusion equation",
      "general core-shell geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}