@article{
 title = {Corrector estimates for a thermodiffusion model with weak thermal coupling},
 type = {article},
 year = {2018},
 keywords = {Composite media,Corrector estimates,Gradient folding operator,Homogenization,Perforated domain,Periodic unfolding,Reaction-diffusion systems,Thermodiffusion},
 volume = {16},
 id = {6faf656d-14bf-3b91-9611-897b3fe81f19},
 created = {2019-08-23T19:37:40.335Z},
 file_attached = {false},
 profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e},
 last_modified = {2019-08-23T19:37:40.335Z},
 read = {false},
 starred = {false},
 authored = {true},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 abstract = {Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermodiffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The term \weak thermal coupling" refers here to the variable scaling in terms of the small homogenization parameter " of the heat conduction-diffusion interaction terms, while the \high-contrast" is considered particularly in terms of the heat conduction properties of the composite material. As a main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling leads to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with "-independent estimates for the thermal and concentration fields and for their coupled fluxes.},
 bibtype = {article},
 author = {Muntean, A. and Reichelt, S.},
 doi = {10.1137/16M109538X},
 journal = {Multiscale Modeling and Simulation},
 number = {2}
}

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The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermodiffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The term \\weak thermal coupling\" refers here to the variable scaling in terms of the small homogenization parameter \" of the heat conduction-diffusion interaction terms, while the \\high-contrast\" is considered particularly in terms of the heat conduction properties of the composite material. As a main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling leads to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with \"-independent estimates for the thermal and concentration fields and for their coupled fluxes.","bibtype":"article","author":"Muntean, A. and Reichelt, S.","doi":"10.1137/16M109538X","journal":"Multiscale Modeling and Simulation","number":"2","bibtex":"@article{\n title = {Corrector estimates for a thermodiffusion model with weak thermal coupling},\n type = {article},\n year = {2018},\n keywords = {Composite media,Corrector estimates,Gradient folding operator,Homogenization,Perforated domain,Periodic unfolding,Reaction-diffusion systems,Thermodiffusion},\n volume = {16},\n id = {6faf656d-14bf-3b91-9611-897b3fe81f19},\n created = {2019-08-23T19:37:40.335Z},\n file_attached = {false},\n profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e},\n last_modified = {2019-08-23T19:37:40.335Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermodiffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The term \\weak thermal coupling\" refers here to the variable scaling in terms of the small homogenization parameter \" of the heat conduction-diffusion interaction terms, while the \\high-contrast\" is considered particularly in terms of the heat conduction properties of the composite material. As a main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling leads to the main mathematical difficulty in the system. 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