On a waveguide with an infinite number of small windows |
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Authors: | Denis Borisov Renata Bunoiu Giuseppe Cardone |
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Institution: | 1. Bashkir State Pedagogical University, October Revolution St. 3a, 450000 Ufa, Russia;2. LMAM, UMR 7122, Université de Metz et CNRS Ile du Saulcy, 57045 Metz cedex 1, France;3. University of Sannio, Department of Engineering, Corso Garibaldi, 107, 82100 Benevento, Italy |
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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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