Gamma-convergence of gradient flows on hilbert and metric spaces and applications

Sylvia Serfaty

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1427-1451
Number of pages25
JournalDiscrete and Continuous Dynamical Systems
Volume31
Issue number4
DOIs
StatePublished - Dec 1 2011

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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

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