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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 9, Pages 1587–1597 (Mi zvmmf4933)  

This article is cited in 8 scientific papers (total in 8 papers)

On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials

D. A. Mironov, Yu. G. Smirnov

Penza State University, ul. Krasnaya 40, Penza, 440026 Russia

Abstract: The problem of determining the permittivity of material samples of arbitrary shape placed in a rectangular waveguide with perfectly conducting walls is investigated. The problem is reduced to solving a nonlinear volume singular integral equation. A theorem on the existence and uniqueness of solutions to the nonlinear volume singular integral equation and of the inverse boundary value problem for determining the permittivity of the material is proved.

Key words: permittivity, Maxwell equations, inverse boundary value problem, volume singular integral equation, contraction principle, computational algorithm.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:9, 1511–1521

Bibliographic databases:

UDC: 519.634
Received: 02.03.2010

Citation: D. A. Mironov, Yu. G. Smirnov, “On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials”, Zh. Vychisl. Mat. Mat. Fiz., 50:9 (2010), 1587–1597; Comput. Math. Math. Phys., 50:9 (2010), 1511–1521

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Shestopalov Yu., Smirnov Yu., “Determination of permittivity of an inhomogeneous dielectric body in a waveguide”, Inverse Problems, 27:9 (2011), 095010  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Medvedik M.Yu., Smirnov Yu.G., “Subhierarchical method for solving problems of diffraction of electromagnetic waves by a dielectric body in a rectangular waveguide”, Journal of Communications Technology and Electronics, 56:8 (2011), 947–952  crossref  isi  isi  elib  scopus
    3. Smirnov Yu.G., Vasyunin D.I., “Iteratsionnyi metod opredeleniya dielektricheskoi pronitsaemosti neodnorodnogo obraztsa materiala”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2011, no. 1, 20–30  elib
    4. Medvedik M.Yu., “Chislennoe reshenie zadachi difraktsii elektromagnitnykh voln na dielektricheskom tele, raspolozhennom v pryamougolnom rezonatore”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2011, no. 3, 22–31  elib
    5. Medvedik M.Yu., “Metod kollokatsii dlya resheniya zadachi difraktsii elektromagnitnykh voln na dielektricheskom tele, raspolozhennom v rezonatore”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2011, no. 2, 28–40  elib
    6. Smirnov Yu.G., Medvedik M.Yu., Grishina E.E., “Iteratsionnyi metod opredeleniya effektivnoi dielektricheskoi pronitsaemosti neodnorodnogo obraztsa materiala”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2011, no. 3, 3–13  elib
    7. Vasyunin D.I., “Raschety dvukhsloinym iteratsionnym metodom dielektricheskoi pronitsaemosti neodnorodnogo obraztsa materiala”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2011, no. 2, 71–79  elib
    8. Grishina E.E., “Chislennyi metod resheniya obratnoi zadachi vosstanovleniya effektivnoi dielektricheskoi pronitsaemosti po koeffitsientu otrazheniya”, Izvestiya vysshikh uchebnykh zavedenii. povolzhskii region. fiziko-matematicheskie nauki, 2012, no. 2, 75–84  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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