WIAS Preprint No. 2499, (2018)

An existence result and evolutionary Gamma-convergence for perturbed gradient systems



Authors

  • Bacho, Aras
  • Emmrich, Etienne
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 35A15 35K50 35K85 49Q20 58E99

Keywords

  • Doubly nonlinear equations, differential inclusions, generalized gradient flows, perturbed gradient flows, evolutionary Gamma convergence, homogenization, reaction-diffusion systems

DOI

10.20347/WIAS.PREPRINT.2499

Abstract

We consider the initial-value problem for the perturbed gradient flows, where a differential inclusion is formulated in terms of a subdifferential of an energy functional, a subdifferential of a dissipation potential and a more general perturbation, which is assumed to be continuous and to satisfy a suitable growth condition. Under additional assumptions on the dissipation potential and the energy functional, existence of strong solutions is shown by proving convergence of a semi-implicit discretization scheme with a variational approximation technique.

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