Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations
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Date
2017-02-23
Authors
Eden, Michael
Muntean, Adrian
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Homogenization, Two-phase thermoelasticity, Corrector estimates, Time-dependent domains, Distributed microstructures
Citation
Eden, M., & Muntean, A. (2017). Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations. <i>Electronic Journal of Differential Equations, 2017</i>(57), pp. 1-21.
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Attribution 4.0 International