Open AccessCombined effects of homogenization and singular perturbations: A bloch wave approach
Author(s) -
Vivek Tewary
Publication year - 2021
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.732
H-Index - 34
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2021012
Subject(s) - homogenization (climate) , bloch wave , eigenvalues and eigenvectors , singular perturbation , mathematical analysis , perturbation (astronomy) , mathematics , spectral gap , physics , quantum mechanics , biodiversity , ecology , biology
In this work, we study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of the periodic heterogeneity. The homogenized tensor is obtained in terms of the first Bloch eigenvalue. The higher Bloch modes do not contribute to the homogenization limit. The main difficulty is the presence of two parameters which requires us to obtain uniform bounds on the Bloch spectral data in various regimes of the parameter.