{
  "id": "2112.14224",
  "version": "v2",
  "published": "2021-12-28T17:18:53.000Z",
  "updated": "2022-01-31T01:57:01.000Z",
  "title": "Perturbations of Parabolic Equations and Diffusion Processes with Degeneration: Boundary Problems, Metastability, and Homogenization",
  "authors": [
    "Mark Freidlin",
    "Leonid Koralov"
  ],
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We study diffusion processes that are stopped or reflected on the boundary of a domain. The generator of the process is assumed to contain two parts: the main part that degenerates on the boundary in a direction orthogonal to the boundary and a small non-degenerate perturbation. The behavior of such processes determines the stabilization of solutions to the corresponding parabolic equations with a small parameter. Metastability effects arise in this case: the asymptotics of solutions, as the size of the perturbation tends to zero, depends on the time scale. Initial-boundary value problems with both the Dirichlet and the Neumann boundary conditions are considered. We also consider periodic homogenization for operators with degeneration.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-01-31T01:57:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boundary problems",
      "degeneration",
      "small non-degenerate perturbation",
      "neumann boundary conditions",
      "metastability effects arise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}