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Homogenization of the Poisson equation in a thick periodic junction. (English) Zbl 0938.35021

Summary: A convergence theorem and asymptotic estimates as \(\varepsilon\to 0\) are proved for a solution to a mixed boundary value problem for the Poisson equation in a junction \(\Omega_\varepsilon\) of a domain \(\Omega_0\) and a large number \(N^2\) of \(\varepsilon\)-periodically situated thin cylinders with thickness of order \(\varepsilon=O ({1\over N})\). For this junction, we construct an extension operator and study its properties.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35B40 Asymptotic behavior of solutions to PDEs
35B25 Singular perturbations in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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