Discrete spectrum of cranked quantum and elastic waveguides
- Autores: Nazarov S.A.1,2,3
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Afiliações:
- St. Petersburg State University
- St. Petersburg State Polytechnical University
- Institute of Problems of Mechanical Engineering
- Edição: Volume 56, Nº 5 (2016)
- Páginas: 864-880
- Seção: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/178453
- DOI: https://doi.org/10.1134/S0965542516050171
- ID: 178453
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Resumo
The spectrum of quantum and elastic waveguides in the form of a cranked strip is studied. In the Dirichlet spectral problem for the Laplacian (quantum waveguide), in addition to well-known results on the existence of isolated eigenvalues for any angle α at the corner, a priori lower bounds are established for these eigenvalues. It is explained why methods developed in the scalar case are frequently inapplicable to vector problems. For an elastic isotropic waveguide with a clamped boundary, the discrete spectrum is proved to be nonempty only for small or close-to-π angles α. The asymptotics of some eigenvalues are constructed. Elastic waveguides of other shapes are discussed.
Sobre autores
S. Nazarov
St. Petersburg State University; St. Petersburg State Polytechnical University; Institute of Problems of Mechanical Engineering
Autor responsável pela correspondência
Email: srgnazarov@yahoo.co.uk
Rússia, Universitetskii pr. 28, Staryi Peterhof, St. Petersburg, 198504; Politekhnicheskaya ul. 29, St. Petersburg, 195251; Bolshoi pr. 61, V.O., St. Petersburg, 199178
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