Abstract
We are concerned with γ-convergence of gradient ows, which is a notion meant to ensure that if a family of energy functionals depending of a parameter Γ-converges, then the solutions to the associated gradient ows converge as well. In this paper we present both a review of the abstract "theory" and of the applications it has had, and a generalization of the scheme to metric spaces which has not appeared elsewhere. We also mention open problems and perspectives.
Original language | English (US) |
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Pages (from-to) | 1427-1451 |
Number of pages | 25 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 31 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2011 |
Keywords
- Allen-cahn equation
- Cahn-hilliard equation
- Gamma-convergence
- Ginzburg-landau equation
- Gradient flow
- Mullins-sekerka
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics