Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774236 | Journal of Differential Equations | 2017 | 32 Pages |
Abstract
We consider the spectral Dirichlet problem for the Laplace operator in the plane Ωâ with double-periodic perforation but also in the domain Ω
- with a semi-infinite foreign inclusion so that the Floquet-Bloch technique and the Gelfand transform do not apply directly. We describe waves which are localized near the inclusion and propagate along it. We give a formulation of the problem with radiation conditions that provides a Fredholm operator of index zero. The main conclusion concerns the spectra Ïâ and Ï
- of the problems in Ωâ and Ω
- , namely we present a concrete geometry which supports the relation Ïââ«Ï
- due to a new non-empty spectral band caused by the semi-infinite inclusion called an open waveguide in the double-periodic medium.
- with a semi-infinite foreign inclusion so that the Floquet-Bloch technique and the Gelfand transform do not apply directly. We describe waves which are localized near the inclusion and propagate along it. We give a formulation of the problem with radiation conditions that provides a Fredholm operator of index zero. The main conclusion concerns the spectra Ïâ and Ï
- of the problems in Ωâ and Ω
- , namely we present a concrete geometry which supports the relation Ïââ«Ï
- due to a new non-empty spectral band caused by the semi-infinite inclusion called an open waveguide in the double-periodic medium.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
G. Cardone, T. Durante, S.A. Nazarov,