IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i11p1862-d1670600.html
   My bibliography  Save this article

Spectral ℝ-Linear Problems: Applications to Complex Permittivity of Coated Cylinders

Author

Listed:
  • Zhanat Zhunussova

    (Institute of Mathematics and Mathematical Modeling, Pushkina St., 125, Almaty 050010, Kazakhstan
    Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Al-Farabi Av., 71, Almaty 050040, Kazakhstan
    Faculty of Computer Technology and Cybersecurity, International Information Technology University, Manasa St., 34/1, Almaty 050040, Kazakhstan
    These authors contributed equally to this work.)

  • Vladimir Mityushev

    (Institute of Mathematics and Mathematical Modeling, Pushkina St., 125, Almaty 050010, Kazakhstan
    Faculty of Computer Science and Telecommunications, Cracow University of Technology, Warszawska St., 24, 31-155 Krakow, Poland
    These authors contributed equally to this work.)

Abstract

A composite-coated inclusion is embedded in a matrix, where the conductivity (permittivity) of the phases is assumed to be complex-valued. The purpose of this paper is to demonstrate that a non-zero flux can arise under specific conditions related to the conductivities of the components in the absence of external sources. These conditions are unattainable with conventional positive conductivities but can be satisfied when the conductivities are negative or complex—a scenario achievable in the context of metamaterials. The problem is formulated as a spectral boundary value problem for the Laplace equation, featuring a linear conjugation condition defined on a smooth curve L . This curve divides the plane R 2 into two regions, D + and D − ∋ ∞ . The spectral parameter appears in the boundary condition, drawing parallels with the Steklov eigenvalue problem. The case of a circular annulus is analyzed using the method of functional equations. The complete set of eigenvalues is derived by applying the classical theory of self-adjoint operators in Hilbert space.

Suggested Citation

  • Zhanat Zhunussova & Vladimir Mityushev, 2025. "Spectral ℝ-Linear Problems: Applications to Complex Permittivity of Coated Cylinders," Mathematics, MDPI, vol. 13(11), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1862-:d:1670600
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/11/1862/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/11/1862/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1862-:d:1670600. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.