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Two-Scale Convergence: Obviousness of the Choice of Test Functions? Not Always

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Shape Optimization, Homogenization and Optimal Control

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 169))

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Abstract

The asymptotic behaviour of a bounded sequence of solutions for some physical problems via the two-scale convergence may not be a direct consequence. In the present example, that is, the homogenization of the weakly damped wave equation (1.1) with initial conditions (1.2), it is shown that the choice of test functions will be more complicated than for the classical homogenization problems.

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Authors and Affiliations

  1. University of Yaounde I, Higher Teachers’ Training College, Yaounde, Cameroon

    Hubert Nnang

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  1. Hubert Nnang
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Correspondence to Hubert Nnang .

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Editors and Affiliations

  1. FB IV Abt. Mathematik, Universität Trier, Trier, Germany

    Volker Schulz

  2. Département de Mathématiques de la, Université Cheikh Anta Diop de Daka, Dakar-Fann, Senegal

    Diaraf Seck

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Nnang, H. (2018). Two-Scale Convergence: Obviousness of the Choice of Test Functions? Not Always. In: Schulz, V., Seck, D. (eds) Shape Optimization, Homogenization and Optimal Control . International Series of Numerical Mathematics, vol 169. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-90469-6_3

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