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Zbl 1003.82007
Garroni, Adriana; Niethammer, Barbara
Correctors and error estimates in the homogenization of a Mullins-Sekerka problem. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 19, No.4, 371-393 (2002). ISSN 0294-1449

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 {\it B. Niethammer} and {\it 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 2000:: *82C26 Dynamic and nonequilibrium phase transitions (general)
35B27 Homogenization, etc.
35R35 Free boundary problems for PDE
80A22 Stefan problems, etc.
74N99 Phase transformations in solids
74Q99 Homogenization, determination of effective properties

Keywords: Mullins-Sekerka free boundary problem; first-order phase transformation

Citations: Zbl 0988.35021

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