Scale-integration and scale-disintegration in nonlinear homogenization (Q1047936)
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scientific article; zbMATH DE number 5655372
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Scale-integration and scale-disintegration in nonlinear homogenization |
scientific article; zbMATH DE number 5655372 |
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Scale-integration and scale-disintegration in nonlinear homogenization (English)
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8 January 2010
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After introducing the reader to his concepts of scale transformations (scale-integration and scale-disintegration), the author deals with the homogenization of a nonlinear PDE model arising in magnetostatics. Basically, a class of coarse-scale problems is derived by integrating a family of two-scale minimization problems (scale-integration) in the presence of appropriate orthogonality conditions. By showing that any solution of the coarse-scale problem can be represented as the fine-scale average of a solution of the two-scale problem (scale-disintegration), the author ensures the equivalence of the two formulations mentioned above.
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two-scale convergence
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\(\Gamma\)-convergence
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periodic unfolding
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magnetostatics
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