A gradient system with a wiggly energy and relaxed EDP-convergence
- Dondl, Patrick
- Frenzel, Thomas
- Mielke, Alexander
2010 Mathematics Subject Classification
- 35K55 35B27 35A15 49S05 49J40 49J45
- Variational evolution, energy functional, dissipation potential, gradient flows, Gamma convergence, EDP-convergence, energy-dissipation, balance, homogenization
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.
- ESAIM Control Optim. Calc. Var., 25 (2019), pp. 68/1--68/45 (published on 05.11.2019), DOI 10.1051/cocv/2018058 .