{
  "id": "2004.02348",
  "version": "v1",
  "published": "2020-04-05T23:18:26.000Z",
  "updated": "2020-04-05T23:18:26.000Z",
  "title": "Nonlocal and nonlinear evolution equations in perforated domains",
  "authors": [
    "Marcone C. Pereira",
    "Silvia Sastre-Gomez"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work we analyze the behavior of the solutions to nonlocal evolution equations of the form $u_t(x,t) = \\int J(x-y) u(y,t) \\, dy - h_\\epsilon(x) u(x,t) + f(x,u(x,t))$ with $x$ in a perturbed domain $\\Omega^\\epsilon \\subset \\Omega$ which is thought as a fixed set $\\Omega$ from where we remove a subset $A^\\epsilon$ called the holes. We choose an appropriated families of functions $h_\\epsilon \\in L^\\infty$ in order to deal with both Neumann and Dirichlet conditions in the holes setting a Dirichlet condition outside $\\Omega$. Moreover, we take $J$ as a non-singular kernel and $f$ as a nonlocal nonlinearity. % Under the assumption that the characteristic functions of $\\Omega^\\epsilon$ have a weak limit, we study the limit of the solutions providing a nonlocal homogenized equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-05T23:18:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear evolution equations",
      "perforated domains",
      "nonlocal evolution equations",
      "dirichlet condition outside",
      "non-singular kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}