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Spectral gaps for periodic piezoelectric waveguides

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Abstract

We construct a family of periodic piezoelectric waveguides Πɛ, depending on a small geometrical parameter, with the following property: as ɛ → +0, the number of gaps in the essential spectrum of the piezoelectricity problem on Πɛ grows unboundedly.

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Authors and Affiliations

  1. Mathematics and Mechanics Faculty, Saint-Petersburg State University, Universitetsky pr., 28, Peterhof, St. Petersburg, Russia, 198504

    Sergei A. Nazarov

  2. Saint-Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, St. Petersburg, Russia, 195251

    Sergei A. Nazarov

  3. Institute of Problems of Mechanical Engineering RAS, V.O., Bolshoj pr., 61, St. Petersburg, Russia, 199178

    Sergei A. Nazarov

  4. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

    Jari Taskinen

Authors
  1. Sergei A. Nazarov
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  2. Jari Taskinen
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Correspondence to Jari Taskinen.

Additional information

The first named author was partially supported by RFFI, Grant 15-01-02175 and by the Academy of Finland Grant No. 127245. The second named author was partially supported by the Academy of Finland project “Functional analysis and applications” and the Väisälä Foundation of the Finnish Academy of Sciences and Letters.

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Nazarov, S.A., Taskinen, J. Spectral gaps for periodic piezoelectric waveguides. Z. Angew. Math. Phys. 66, 3017–3047 (2015). https://doi.org/10.1007/s00033-015-0561-7

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  • DOI: https://doi.org/10.1007/s00033-015-0561-7

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