| Abstract: |
| Phase transition processes (e.g, between different phases in steel) are typical examples of problems where the geometry is allowed to evolve and where microscopic effects (growing nucleation cells) are essential for an understanding of the macroscopic properties of the system.
In this talk, we present and analyze a Stefan type model describing such phase transition processes. Starting with a prescribed normal velocity of the interface separating the competing phases, a specific transformation of coordinates, the so-called Hanzawa transformation, is constructed. This is achieved by (i) solving a non-linear system of ODEs characterizing the motion of the interface and (ii) using the Implicit Function Theorem to arrive at the height function characterizing this motion.
Based on uniform estimates for the functions related to the transformation of coordinates, the strong two-scale convergence of these functions is shown. Finally, these results are used to establish the corresponding effective model. |
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