{
  "annotation_id": "12a11570-b516-4230-bf2e-354bc4297fb3",
  "date_created": "2026-02-17T05:53:04.333000Z",
  "date_modified": "2026-02-17T05:53:04.333000Z",
  "file_hash": "8800f046402be21efcf17f6ab1ee7e331d8f1243415730f8cdeab9f3481e3ae0",
  "private": false,
  "record": {
    "abstract": "We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a phase-field. We investigate both the case of an independently evolving phase-field and of coupled phase-field evolution driven by a viscous Hamilton-Jacobi equation. Such systems are used in the modelling of single-cell chemotaxis, where the contour of the cell shape corresponds to a level set of the phase-field. The technical challenge lies in the singularities at zero level sets of the phase-field. For large classes of initial data, we establish global existence of probabilistically weak solutions in $L^2$-spaces with weights which compensate for the singularities.",
    "arxiv_id": "2601.05881",
    "authors": [
      "Amjad Saef",
      "Wilhelm Stannat"
    ],
    "categories": [
      "math.PR",
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On a stochastic phase-field model of cell motility with singular diffusion",
    "url": "https://arxiv.org/abs/2601.05881",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "af090b14-d474-4be3-9f61-8744aa04bcad",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}