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Correctors and error estimates in the homogenization of a Mullins-Sekerka problem. (English) Zbl 1003.82007

Summary: We study the homogenization of a Mullins-Sekerka free boundary problem which serves as a model for coarsening of nuclei in a first-order phase transformation. We consider a regime where the volume fraction of the nuclei is small but screening effects are not negligible. The limit equation was recently derived by B. Niethammer and F. Otto [Calc. Var. Partial Differ. Equ. 13, 33-68 (2001; Zbl 0988.35021)]. We improve this convergence result by constructing correctors and providing error estimates in terms of the volume fraction. This yields in particular an asymptotic expansion for the growth rate of the nuclei.

MSC:

82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
74N99 Phase transformations in solids
74Q99 Homogenization, determination of effective properties in solid mechanics

Citations:

Zbl 0988.35021
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References:

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