{
  "id": "2506.17094",
  "version": "v1",
  "published": "2025-06-20T16:02:22.000Z",
  "updated": "2025-06-20T16:02:22.000Z",
  "title": "Nonlinear random perturbations of Reaction-Diffusion Equations",
  "authors": [
    "Sandra Cerrai",
    "Giuseppina Guatteri",
    "Gianmario Tessitore"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and non-locally on the solution through a conditional expectation. The reaction term is assumed to be merely continuous and to satisfy a quasi-dissipativity condition, without requiring any growth bounds or local Lipschitz continuity. This setting introduces significant analytical challenges due to the temporal non-locality and the lack of regularity assumptions. Our results represent a substantial advance in the study of nonlinear stochastic perturbations of SPDEs, extending the framework developed in a previous paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-20T16:02:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear random perturbations",
      "reaction-diffusion equations",
      "stochastic partial differential equations",
      "local lipschitz continuity",
      "nonlinear stochastic perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}