WIAS Preprint No. 2459, (2017)

A gradient system with a wiggly energy and relaxed EDP-convergence



Authors

  • Dondl, Patrick
  • Frenzel, Thomas
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 35K55 35B27 35A15 49S05 49J40 49J45

Keywords

  • Variational evolution, energy functional, dissipation potential, gradient flows, Gamma convergence, EDP-convergence, energy-dissipation, balance, homogenization

DOI

10.20347/WIAS.PREPRINT.2459

Abstract

If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic system. We introduce a notion of evolutionary Gamma-convergence that relates the microscopic energy and the microscopic dissipation potential with their macroscopic limits via Gamma-convergence. We call this notion relaxed EDP-convergence since the special structure of the dissipation functional may not be preserved under Gamma-convergence. However, by investigating the kinetic relation we derive the macroscopic dissipation potential.

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