On a waveguide with an infinite number of small windows

Abstract : We consider a waveguide modeled by the Laplacian in a straight planar strip with the Dirichlet condition on the upper boundary, while on the lower one we impose periodically alternating boundary conditions with a small period. We study the case when the homogenization leads us to the Neumann boundary condition on the lower boundary. We establish the uniform resolvent convergence and provide the estimates for the rate of convergence. We construct the two-terms asymptotics for the first band functions of the perturbed operator and also the complete two-parametric asymptotic expansion for the bottom of its spectrum.
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Article dans une revue
Comptes Rendus Mathématique, Elsevier Masson, 2011, 349 (1-2), pp.53-56. 〈10.1016/j.crma.2010.11.029〉
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https://hal.inria.fr/hal-01283615
Contributeur : Renata Bunoiu <>
Soumis le : samedi 5 mars 2016 - 19:14:39
Dernière modification le : jeudi 11 janvier 2018 - 06:26:21

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Denis Borisov, Renata Bunoiu, Giuseppe Cardone. On a waveguide with an infinite number of small windows. Comptes Rendus Mathématique, Elsevier Masson, 2011, 349 (1-2), pp.53-56. 〈10.1016/j.crma.2010.11.029〉. 〈hal-01283615〉

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