Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows

Abstract : We consider a planar waveguide modeled by the Laplacian in a straight infinite strip with the Dirichlet boundary condition on the upper boundary and with frequently alternating boundary conditions (Dirichlet and Neumann) on the lower boundary. The homogenized operator is the Laplacian subject to the Dirichlet boundary condition on the upper boundary and to the Dirichlet or Neumann condition on the lower one. We prove the uniform resolvent convergence for the perturbed operator in both cases and obtain the estimates for the rate of convergence. Moreover, we construct the leading terms of the asymptotic expansions for the first band functions and the complete asymptotic expansion for the bottom of the spectrum.
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International Journal of Applied Mathematical Sciences, 2011, 176 (6), pp.774-785. 〈10.1007/s10958-011-0435-2〉
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Contributeur : Renata Bunoiu <>
Soumis le : samedi 5 mars 2016 - 19:07:16
Dernière modification le : jeudi 11 janvier 2018 - 06:26:21

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D Borisov, R Bunoiu, G Cardone. Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows. International Journal of Applied Mathematical Sciences, 2011, 176 (6), pp.774-785. 〈10.1007/s10958-011-0435-2〉. 〈hal-01283614〉

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