Acoustical Physics

, Volume 59, Issue 6, pp 633–639 | Cite as

Obstacles in acoustic waveguides becoming “invisible” at given frequencies

Classical Problems of Linear Acoustics and Wave Theory

Abstract

We prove the existence of gently sloping perturbations of walls of an acoustic two-dimensional waveguide, for which several waves at given frequencies pass by the created obstacle without any distortion or with only a phase shift.

Keywords

acoustic waveguide scattering invisible scatterer asymptotic analysis 

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References

  1. 1.
    Yu. I. Bobrovnitskii, Acoust. Phys. 50, 647 (2004).ADSCrossRefGoogle Scholar
  2. 2.
    Yu. I. Bobrovnitskii, Acoust. Phys. 53, 535 (2007).ADSCrossRefGoogle Scholar
  3. 3.
    A. Greenleaf, Ya. Kurylev, M. Lassas, and G. Uhlmann, Bull. Amer. Math. Soc. 46, 55 (2009).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    L. Bourgeois and E. Lunéville, Inverse Problems 24, 015018 (2008).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    S. A. Nazarov, Theor. Mathem. Phys. 167, 606 (2011).CrossRefMATHGoogle Scholar
  6. 6.
    S. A. Nazarov, Acoust. Phys. 57, 764 (2011).ADSCrossRefGoogle Scholar
  7. 7.
    V. Pagneux and A. Maurel, J. Acoust. Soc. Am. 116, 1913 (2004).ADSCrossRefGoogle Scholar
  8. 8.
    W. G. Mazja and S. A. Nasarow, and B. A. Plamenewski, Asymptotische Theorie Elliptischer Randwertaufgaben in singular gestreten Gebieten (Akademie-Verlag, Berlin, 1991); English translation: Maz’ya V., Nazarov S., Plamenevskij B. Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. (Birkhäuser Verlag, Basel, 2000).Google Scholar
  9. 9.
    S. A. Nazarov, Acoust. Phys. 58, 633 (2012).ADSCrossRefGoogle Scholar
  10. 10.
    S. A. Nazarov and B. A. Plamenevsky, Elliptic Problems in Domains with Piecewise Smooth Boundaries (Walter de Gruyter, Berlin, 1994).CrossRefMATHGoogle Scholar
  11. 11.
    S. A. Nazarov, Russ. Mathem. Bull. 54, 947 (1999).MATHGoogle Scholar
  12. 12.
    S. A. Nazarov, in Sobolev Spaces in Mathematics. Vol. 2, Ed by W. G. Mazja, (Springer-Verlag, New York, 2008).Google Scholar
  13. 13.
    Kato, T., Perturbation Theory for Linear Operators (Springer-Verlag, Berlin, 1966).CrossRefMATHGoogle Scholar
  14. 14.
    E. Hille and R. Fillips, Proc. Amer. Math. Soc. Colloq. vol. 31, 1957.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.POEMS (UMR 7231 CNRS-ENSTA-INRIA), ENSTAPalaiseauFrance
  2. 2.Mathematics and Mechanics FacultySt. Petersburg State UniversityPeterhof, St. PetersburgRussia

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