CORRECTOR ESTIMATES FOR THE HOMOGENIZATION OF A TWO-SCALE THERMOELASTICITY PROBLEM WITH A PRIORI KNOWN PHASE TRANSFORMATIONS

Michael Eden, Adrian Muntean
2017 Electronic Journal of Differential Equations   unpublished
We investigate corrector estimates for the solutions of a thermoe-lasticity 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
more » ... o 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.
fatcat:ifi3fmehkjdhnepj7nkffk34vq