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arXiv · 1610.00945

Corrector estimates for a thermo-diffusion model with weak thermal coupling

Adrian Muntean·Sina Reichelt
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Abstract

The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The terminology "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 thought particularly in terms of the heat conduction properties of the composite material. As 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 lead to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with a priori estimates for the thermal and concentration fields and for their coupled fluxes.

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Adrian Muntean, Sina Reichelt. 2016-10-04. Corrector estimates for a thermo-diffusion model with weak thermal coupling. https://arxiv.org/abs/1610.00945

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