{
  "id": "2401.08400",
  "version": "v2",
  "published": "2024-01-16T14:42:11.000Z",
  "updated": "2024-06-24T06:51:02.000Z",
  "title": "Well-posedness of a bulk-surface convective Cahn--Hilliard system with dynamic boundary conditions",
  "authors": [
    "Patrik Knopf",
    "Jonas Stange"
  ],
  "journal": "Nonlinear Differ. Equ. Appl. 31, 82 (2024)",
  "doi": "10.1007/s00030-024-00970-3",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a general class of bulk-surface convective Cahn--Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn--Hilliard type allow for dynamic changes of the contact angle between the diffuse interface and the boundary, a convection-induced motion of the contact line as well as absorption of material by the boundary. The coupling conditions for bulk and surface quantities involve parameters $K,L\\in[0,\\infty]$, whose choice declares whether these conditions are of Dirichlet, Robin or Neumann type. We first prove the existence of a weak solution to our model in the case $K,L\\in (0,\\infty)$ by means of a Faedo--Galerkin approach. For all other cases, the existence of a weak solution is then shown by means of the asymptotic limits, where $K$ and $L$ are sent to zero or to infinity, respectively. Eventually, we establish higher regularity for the phase-fields, and we prove the uniqueness of weak solutions given that the mobility functions are constant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-24T06:51:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K35",
      "35D30",
      "35A01",
      "35A02",
      "35Q92"
    ],
    "keywords": [
      "bulk-surface convective cahn-hilliard system",
      "dynamic boundary conditions",
      "weak solution",
      "well-posedness",
      "classical neumann boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}