Cioranescu, D.; Donato, P.; Murat, F.; Zuazua, E. Homogenization and corrector for the wave equation in domains with small holes. (English) Zbl 0807.35077 Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 18, No. 2, 251-293 (1991). From the introduction: We study the homogenization of the wave equation with Dirichlet boundary conditions in perforated domains with small holes. Let \(\Omega\) be a fixed bounded domain of \(\mathbb{R}^ n\) \((n \geq 2)\). Denote by \(\Omega_ \varepsilon\) the domain obtained by removing from \(\Omega\) a set \(S_ \varepsilon = \cup^{N (\varepsilon)}_{i = 1} S^ i_ \varepsilon\) of \(N(\varepsilon)\) closed subsets of \(\Omega\) (here, \(\varepsilon > 0\) denotes a parameter which takes its values in a sequence which tends to zero while \(N(\varepsilon)\) tends to infinity). Finally let \(T>0\) be fixed. We consider the wave equation \[ u_ \varepsilon'' - \Delta u_ \varepsilon = f_ \varepsilon \text{ in } \Omega_ \varepsilon \times (0,T), \quad u_ \varepsilon = 0 \text{ on } \partial \Omega_ \varepsilon \times (0,T), \quad u_ \varepsilon (0) = u^ 0_ \varepsilon,\;u_ \varepsilon'(0) = u^ 1_ \varepsilon \text{ in } \Omega_ \varepsilon. \] Our aim is to describe the convergence of the solutions \(u_ \varepsilon\), to identify the equation satisfied by the limit \(u\) and to give corrector results. Cited in 3 ReviewsCited in 7 Documents MSC: 35L05 Wave equation 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure Keywords:perforated domains with small holes PDFBibTeX XMLCite \textit{D. Cioranescu} et al., Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 18, No. 2, 251--293 (1991; Zbl 0807.35077) Full Text: Numdam EuDML References: [1] S. Brahim-Otsmane - G.A. Francfort - F. Murat , Correctors for the homogenization of the wave and heat equations , J. Math. 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