{
  "id": "2405.18034",
  "version": "v1",
  "published": "2024-05-28T10:38:27.000Z",
  "updated": "2024-05-28T10:38:27.000Z",
  "title": "Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations",
  "authors": [
    "Matej Benko",
    "Iwona Chlebicka",
    "Jørgen Endal",
    "Błażej Miasojedow"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "stat.CO"
  ],
  "abstract": "We study the spatially homogeneous granular medium equation \\[\\partial_t\\mu=\\rm{div}(\\mu\\nabla V)+\\rm{div}(\\mu(\\nabla W \\ast \\mu))+\\Delta\\mu\\,,\\] within a large and natural class of the confinement potentials $V$ and interaction potentials $W$. The considered problem do not need to assume that $\\nabla V$ or $\\nabla W$ are globally Lipschitz. With the aim of providing particle approximation of solutions, we design efficient forward-backward splitting algorithms. Sharp convergence rates in terms of the Wasserstein distance are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-28T10:38:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence rates",
      "particle approximation",
      "spatially homogeneous granular medium equation",
      "design efficient forward-backward splitting algorithms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}