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Homogenization of Cahn–Hilliard‐type equations with unbounded potentials
Author(s) -
Liero Matthias,
Reichelt Sina
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610447
Subject(s) - homogenization (climate) , regular polygon , mathematics , dissipation , convergence (economics) , variational inequality , type (biology) , focus (optics) , energy functional , mathematical analysis , physics , thermodynamics , geometry , economics , biodiversity , ecology , biology , economic growth , optics
In this note we recall two approaches to evolutionary Γ‐convergence for classical gradient systems: evolutionary variational inequalities versus energy‐dissipation principles. Following [1] we apply both approaches to homogenize Cahn–Hilliard‐type equations with rapidly oscillating coefficients and quite general potential. Here the focus is on the Γ‐convergence of the energy functional, which we prove without assuming any growth conditions for the convex part of the potential. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)