{
  "id": "2407.19301",
  "version": "v1",
  "published": "2024-07-27T17:11:00.000Z",
  "updated": "2024-07-27T17:11:00.000Z",
  "title": "A probabilistic interpretation of a non-conservative and path-dependent nonlinear reaction-diffusion system for the marble sulphation in Cultural Heritage",
  "authors": [
    "Daniela Morale",
    "Leonardo Tarquini",
    "Stefania Ugolini"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Given a reaction-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation using a non-Markovian McKean-type stochastic differential equation. We discuss the well-posedness of such a stochastic model, and we establish the propagation of chaos property for the related interacting particle system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-27T17:11:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H30",
      "60J60",
      "65C35",
      "58J35"
    ],
    "keywords": [
      "path-dependent nonlinear reaction-diffusion system",
      "probabilistic interpretation",
      "mckean-type stochastic differential equation",
      "cultural heritage",
      "marble sulphation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}