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Asymptotics for the Spectrum of a Floquet-Parametric Family of Homogenization Problems Associated with a Dirichlet Waveguide

In: Integral Methods in Science and Engineering

Author

Listed:
  • D. Gómez

    (Universidad de Cantabria)

  • S. A. Nazarov

    (St. Petersburg State University)

  • R. Orive-Illera

    (Universidad Autónoma de Madrid)

  • M. -E. Pérez-Martínez

    (Universidad de Cantabria)

Abstract

In this chapter, we address the asymptotic behavior of the eigenvalues and eigenfunctions of a parametric family of problems for the Laplace operator posed on a rectangular perforated domain of the plane. The perforations are periodically placed along the ordinate axis. The two parameters of the problem are the period, which converges toward zero, and the so-called Floquet parameter. The boundary conditions are quasi-periodicity conditions on the lateral sides of the rectangle and Dirichlet over the rest. In particular, we provide bounds for convergence rates of the eigenvalues which are uniform in both parameters.

Suggested Citation

  • D. Gómez & S. A. Nazarov & R. Orive-Illera & M. -E. Pérez-Martínez, 2022. "Asymptotics for the Spectrum of a Floquet-Parametric Family of Homogenization Problems Associated with a Dirichlet Waveguide," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Paul J. Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 95-111, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-07171-3_7
    DOI: 10.1007/978-3-031-07171-3_7
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