{
  "id": "1605.00801",
  "version": "v1",
  "published": "2016-05-03T09:21:21.000Z",
  "updated": "2016-05-03T09:21:21.000Z",
  "title": "A variational principle for nonpotential perturbations of gradient flows of nonconvex energies",
  "authors": [
    "Stefano Melchionna"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the minimization of a parameter-dependent functional over entire trajectories and a fixed-point argument. These regularized solutions converge up to subsequence to solutions of the gradient flow as the regularization parameter goes to zero. Applications of the abstract theory to nonlinear reaction-diffusion systems are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-03T09:21:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K57",
      "49J27"
    ],
    "keywords": [
      "gradient flow",
      "nonpotential perturbations",
      "nonconvex energies",
      "variational principle",
      "nonlinear reaction-diffusion systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}