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A system of integro-differential equations of electrodynamics and the inverse laplace transform

  • Magnetic Methods
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Russian Journal of Nondestructive Testing Aims and scope Submit manuscript

Abstract

A system of integro-differential equations of electrodynamics for the electromagnetic field in a conducting specimen is considered under certain assumptions with regard to the properties of this specimen, the environment, and the density of the external current. It is proved that the studied system of equations has a unique solution, to which the inverse Laplace transform can be applied. The application of perturbation theory to calculating the electric and magnetic fields on a small change in the electrical conductivity is considered.

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References

  1. Tamm, I.E., Osnovy Teorii Elektrichestva (Fundamentals of the Theory of Electricity), Moscow: Nauka, 1989.

    Google Scholar 

  2. Lavrent’ev, M.A. and Shabat, B.V., Metody teorii funktsii kompleksnoi peremennoi (Methods of the Theory of Functions of a Complex Variable), Moscow: Nauka, 1973.

    Google Scholar 

  3. Dyakin, V.V. and Raevskii, V.Ya., Direct and Inverse Problems of Classical Electrodynamics, Defektoskopiya, 1996, no. 10, pp. 31–39.

  4. Marvin, S.V. and Dyakin, V.V., On Existence and Uniqueness of the Solution of Initial-Value Boundary Problem of Electrodynamics, Vestn. UGTU-UPI, 2005, vol. 69, no. 17, pp. 295–302.

    Google Scholar 

  5. Mikhlin, S.G., Lektsii po lineinym integral’nym uravneniyam (Lectures on Linear Integral Equations), Moscow: Fizmatgiz, 1959.

    Google Scholar 

  6. Dyakin, V.V. and Raevskii, V.Ya., Analysis of a System of Electrodynamic Integro-Differential Equations with Constant Parameters of Media, Zh. Vychisl. Mat. Mat. Fiz., 2001, vol. 41, no. 9, pp. 1416–1421 [Comput. Math. Math. Phys. (Engl. Transl.), vol. 41, no. 9, pp. 1346–1350].

    Google Scholar 

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Authors and Affiliations

  1. Ural State Technical University, ul. Mira 19, Yekaterinburg, 620002, Russia

    S. V. Marvin

  2. Institute of Metal Physics, Ural Division, Russian Academy of Sciences, ul. Sof’i Kovalevskoi 18, Yekaterinburg, 620041, Russia

    V. V. Dyakin

Authors
  1. S. V. Marvin
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  2. V. V. Dyakin
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Additional information

Original Russian Text © S.V. Marvin, V.V. Dyakin, 2008, published in Defektoskopiya, 2008, Vol. 44, No. 3, pp. 30–36.

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Marvin, S.V., Dyakin, V.V. A system of integro-differential equations of electrodynamics and the inverse laplace transform. Russ J Nondestruct Test 44, 178–183 (2008). https://doi.org/10.1134/S1061830908030030

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  • DOI: https://doi.org/10.1134/S1061830908030030

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