{
  "id": "2312.01863",
  "version": "v1",
  "published": "2023-12-04T12:49:46.000Z",
  "updated": "2023-12-04T12:49:46.000Z",
  "title": "Cauchy problem for singular-degenerate porous medium type equations: well-posedness and Sobolev regularity",
  "authors": [
    "Nick Lindemulder",
    "Stefanie Sonner"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Motivated by models for biofilm growth, we consider Cauchy problems for quasilinear reaction diffusion equations where the diffusion coefficient has a porous medium type degeneracy as well as a singularity. We prove results on the well-posedness and Sobolev regularity of solutions. The proofs are based on m-accretive operator theory, kinetic formulations and Fourier analytic techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-04T12:49:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K59",
      "35K65",
      "35K67",
      "35B65",
      "46E35",
      "47H05"
    ],
    "keywords": [
      "singular-degenerate porous medium type equations",
      "sobolev regularity",
      "cauchy problem",
      "well-posedness",
      "quasilinear reaction diffusion equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}