Electron. J. Differential Equations,
Vol. 2017 (2017), No. 57, pp. 121.
Corrector estimates for the homogenization of a twoscale thermoelasticity
problem with a priori known phase transformations
Michael Eden, Adrian Muntean
Abstract:
We investigate corrector estimates for the solutions of a thermoelasticity
problem posed in a highly heterogeneous twophase medium and its
corresponding twoscale thermoelasticity model which was derived in [11]
by twoscale 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 twoscale 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; twophase thermoelasticity; corrector estimates;
timedependent 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.unibremen.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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