{
  "id": "1803.06953",
  "version": "v1",
  "published": "2018-03-19T14:35:55.000Z",
  "updated": "2018-03-19T14:35:55.000Z",
  "title": "Entropy solutions for stochastic porous media equations",
  "authors": [
    "Konstantinos Dareiotis",
    "Maté Gerencsér",
    "Benjamin Gess"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well - posedness and $L_1$-contraction is obtained in the class of entropy solutions. Our scope allows for porous medium operators $\\Delta (|u|^{m-1}u)$ for all $m\\in(1,\\infty)$, and H\\\"older continuous diffusion nonlinearity with exponent $1/2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-19T14:35:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35K65",
      "35K59"
    ],
    "keywords": [
      "stochastic porous media equations",
      "entropy solutions",
      "continuous diffusion nonlinearity",
      "porous medium-type equations",
      "entropy formulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}