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On the Polarization Matrix for a Perforated Strip

In: Integral Methods in Science and Engineering

Author

Listed:
  • Sergey A. Nazarov

    (St. Petersburg State University
    Institute of Problems of Mechanical Engineering RAS)

  • Rafael Orive-Illera

    (Universidad Autónoma de Madrid)

  • María-Eugenia Pérez-Martínez

    (Universidad de Cantabria)

Abstract

We consider a boundary value problem for the harmonic functions in an unbounded perforated strip Π ∖ ω ¯ $$\varPi \setminus \overline \omega $$ , ω being the “Dirichlet hole”, namely a bounded Lipschitz domain of ℝ $${\mathbb R}$$ , where a Dirichlet condition is prescribed. The other boundary conditions are periodicity conditions on the lateral boundary of Π = (0, H) × (−∞, ∞). We study properties of the coefficients of the so-called polarization matrix, while we highlight the dependence of these coefficients on the dimensions of the hole by means of two examples.

Suggested Citation

  • Sergey A. Nazarov & Rafael Orive-Illera & María-Eugenia Pérez-Martínez, 2019. "On the Polarization Matrix for a Perforated Strip," Springer Books, in: Christian Constanda & Paul Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 267-281, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-16077-7_21
    DOI: 10.1007/978-3-030-16077-7_21
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