Deterministic homogenization of integral functionals with convex integrands |
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Authors: | Gabriel Nguetseng Hubert Nnang Jean Louis Woukeng |
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Affiliation: | 1. Department of Mathematics, University of Yaounde 1, P.O. Box 812, Yaounde, Cameroon 2. école Normale Supérieure, P.O. Box 47, Yaounde, Cameroon 3. Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67, Dschang, Cameroon 4. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 002, South Africa
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Abstract: | In order to widen the scope of the applications of deterministic homogenization, we consider here the homogenization problem for a family of integral functionals. The homogenization procedure tending to be classical, the choice focused on the convex integral functionals is made just to simplify the presentation of the paper. We use a new approach based on the Stepanov type spaces, which approach allows us to solve various problems such as the almost periodic homogenization problem and others without resorting to additional assumptions. We then apply it to obtain a general homogenization result and then we provide a number of physical applications of the result. The convergence method used falls within the scope of two-scale convergence. |
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