# Effective behavior of an interface propagating through a periodic elastic medium

@article{Dondl2012EffectiveBO,
title={Effective behavior of an interface propagating through a periodic elastic medium},
author={P. Dondl and K. Bhattacharya},
journal={arXiv: Analysis of PDEs},
year={2012}
}
• Published 2012
• Mathematics
• arXiv: Analysis of PDEs
We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the graph of the function $g$ which evolves according to the equation $g_t (x) = -(-\Delta)^{1/2}g (x) + \varphi(x, g(x)) + F$. This equation also arises in the study of dislocations and fracture. We show in the periodic setting that such interfaces exhibit a stick… Expand

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