Geodesic
Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy
Andrea Braides1 orcid ; Caterina Ida Zeppieri2
1Università di Roma Tor Vergata, Italy
2SISSA, Trieste, Italy
Interfaces and free boundaries, Tome 11 (2009) no. 1, pp. 61-118

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DOI

The combined effect of fine heterogeneities and small gradient perturbations is analyzed by means of an asymptotic development by Γ-convergence for a family of energies related to (one-dimensional) phase transformations. We show that multi-scale effects add up to the usual sharp-interface limit, due to the homogenization of microscopic interfaces, internal and external boundary layers, optimal arrangements of microscopic oscillations, etc. Several regimes are analyzed depending on the “size” of the heterogeneity (small or large perturbations of a homogeneous situation) and their relative period as compared with the characteristic length of the phase transitions (slow or fast oscillations).
DOI : 10.4171/ifb/204
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Γ-convergence, Γ-development, phase transitions, homogenization

Andrea Braides  1   ; Caterina Ida Zeppieri  2

1 Università di Roma Tor Vergata, Italy
2 SISSA, Trieste, Italy 
Andrea Braides; Caterina Ida Zeppieri. Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy. Interfaces and free boundaries, Tome 11 (2009) no. 1, pp. 61-118. doi: 10.4171/ifb/204
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