Exploring families of energy-dissipation landscapes via tilting -- Three types of EDP convergence
- Mielke, Alexander
- Montefusco, Alberto
- Peletier, Mark A.
2010 Mathematics Subject Classification
- 49S05 47J30 35K55 35A15 49J45
- Gradient systems, energy-dissipation principle, wiggly-energy model, wiggly-dissipation model, simple EDP convergence, EDP convergence with tilting, contact EDP convergence with tilting
This paper revolves around a subtle distinction between two concepts: passing to the limit in a family of gradient systems, on one hand, and deriving effective kinetic relations on the other. The two concepts are strongly related, and in many examples they even appear to be the same. Our main contributions are to show that they are different, to show that well-known techniques developed for the former may give incorrect results for the latter, and to introduce new tools to remedy this. The approach is based on the Energy-Dissipation Principle that provides a variational formulation to gradient-flow equations that allows one to apply techniques from Γ-convergence of functional on states and functionals on trajectories.