Electron. J. Differential Equations, Vol. 2017 (2017), No. 57, pp. 1-21.

Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations

Michael Eden, Adrian Muntean

We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in [11] by two-scale convergence arguments. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing a priori known phase transformations. While such estimates seem not to be obtainable in the fully coupled setting, we show that for some simplified scenarios optimal convergence rates can be proven rigorously. The main technique for the proofs are energy estimates using special reconstructions of two-scale functions and particular operator estimates for periodic functions with zero average. Here, additional regularity results for the involved functions are necessary.

Submitted February 12, 2017. Published February 23, 2017.
Math Subject Classifications: 35B27, 35B40, 74F05.
Key Words: Homogenization; two-phase thermoelasticity; corrector estimates; time-dependent domains; distributed microstructures.

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Michael Eden
Center for Industrial Mathematics, FB 3
University of Bremen
Bibliotheksstr. 1, 28359
Bremen, Germany
email: leachim@math.uni-bremen.de
Adrian Muntean
Department of Mathematics and Computer Science
University of Karlstad
Universitetsgatan 2
651 88 Karlstad, Sweden
email: adrian.muntean@kau.se

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