Skip to main content
SpringerLink
Log in

On Generalized Solutions of the Problems of Electromagnetic Wave Diffraction in the Open Space

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this article we construct a special class of the generalized functions for the rigorous justification of joining method of solving some diffraction problems of electromagnetic waves by thin conducting screens. Linear functionals on a set of linear combinations of Hermit functions are considered as the generalized functions. The traces of the solutions of Helmholtz equation on the plane are interpreted in the generalized sense. The infinite sets of linear algebraic equations are derived directly from the generalized boundary conditions. The results of the computing experiment are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

REFERENCES

  1. N. B. Pleshchinskii, ‘‘On generalized solutions of problems of electromagnetic wave diffraction by screens in the closed cylindrical waveguide,’’ Lobachevskii J. Math. 40 (1), 201–209 (2019).

    Article  MathSciNet  Google Scholar 

  2. V. S. Mokeichev and A. V. Mokeichev, ‘‘New approach to theorie of linear problems for sets of partial differential equations, I,’’ Izv. Vyssh. Uchebn. Zaved., Mat. 1, 25–35 (1999).

    Google Scholar 

  3. H. Bateman and A. Erdélyi, Higher Transcendental Function (McGraw-Hill, New York, 1953), Vol. 2.

    MATH  Google Scholar 

  4. L. Schwarz, Theorie des distributions (Hermann, Paris, 1966).

    Google Scholar 

  5. V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1988) [in Russian].

    MATH  Google Scholar 

  6. H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer, Berlin, 1961) [in German].

    Google Scholar 

  7. A. S. Ilyinsky and Yu. G. Smirnov, Electromagnetic Wave Diffraction by Conducting Screens: Pseudodifferential Operators in Diffraction Problems (VSP, Utrecht, Nederlands, 1998).

Download references

Funding

This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program.

Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Information Technologies, Kazan (Volga Region) Federal University, 420008, Kazan, Tatarstan, Russia

    N. B. Pleshchinskii

Authors
  1. N. B. Pleshchinskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. B. Pleshchinskii.

Additional information

(Submitted by E. E. Tyrtyshnikov)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pleshchinskii, N.B. On Generalized Solutions of the Problems of Electromagnetic Wave Diffraction in the Open Space. Lobachevskii J Math 42, 1391–1401 (2021). https://doi.org/10.1134/S1995080221060238

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080221060238

Keywords:

Search

Navigation