{
  "abstract": "We investigate stochastic mean-field Schrödinger-type equations driven by complex-valued porousmedium operators, with nonhomogeneous random Dirichlet boundary conditions and law dependence in both drift and diffusion coefficients. We prove existence and uniqueness of strong solutions by combining a lifting of the random boundary datum, monotonicity methods, Galerkin approximations, and a fixed-point argument for the associated measure flow. This extends existing well-posedness results by allowing a law-dependent diffusion coefficient and random nonhomogeneous boundary data. We also prove exact controllability for a class of finite-dimensional linear mean-field stochastic differential equations with possibly degenerate diffusion controls. The result relies on a Gramian condition for the mean dynamics and a range-inclusion condition compensating for the degenerate directions. Modal reductions of linear stochastic Schrödinger-type equations illustrate the connection between the two settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Gabriel Brehuescu"
    },
    {
      "name": "Dan Goreac"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bn6d1y0vp8sne.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "bn6d1y0vp8sne",
  "issns": [],
  "landing_url": "https://univ-eiffel.hal.science/hal-05795670v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://univ-eiffel.hal.science/hal-05795670/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bn6d1y0vp8sne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:55Z",
      "native_id": "hal-05795670",
      "source": "hal",
      "url": "https://univ-eiffel.hal.science/hal-05795670v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Well-Posedness of Stochastic Mean-Field Schrödinger Porous-Medium Equations and Control of Their Modal Reductions",
  "title_text": "Well-Posedness of Stochastic Mean-Field Schrödinger Porous-Medium Equations and Control of Their Modal Reductions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:55Z",
  "url": "https://research.draconitic.com/paper/bn6d1y0vp8sne",
  "venue": "HAL",
  "versions": []
}