{
  "annotation_id": "654fe348-2b27-40f1-b1ff-e0a4f84f73e3",
  "date_created": "2026-03-02T18:00:29.387000Z",
  "date_modified": "2026-03-02T18:00:29.387000Z",
  "file_hash": "9bc3c2b523226e44fc3ac51f4676f4df2f627ab6a44616733433f80020dd715f",
  "private": false,
  "record": {
    "abstract": "We study properties of the solutions of a family of second order\nintegro-differential equations, which describe the large scale dynamics of a\nclass of microscopic phase segregation models with particle conserving\ndynamics. We first establish existence and uniqueness as well as some\nproperties of the instantonic solutions. Then we concentrate on formal\nasymptotic (sharp interface) limits. We argue that the obtained interface\nevolution laws (a Stefan-like problem and the Mullins-Sekerka solidification\nmodel) coincide with the ones which can be obtained in the analogous limits\nfrom the Cahn-Hilliard equation, the fourth order PDE which is the standard\nmacroscopic model for phase segregation with one conservation law.",
    "arxiv_id": "patt-sol/9705001",
    "authors": [
      "G. Giacomin",
      "J. L. Lebowitz"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "title": "Phase Segregation Dynamics In Particle Systems with Long Range   Interactions II: Interface motion",
    "url": "https://arxiv.org/abs/patt-sol/9705001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "562032f3-07d2-4de3-bcf3-4c58764619c1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}