Abstract
An initial-boundary value problem of electrodynamics is considered for a flawed metal ferromagnetic body that is placed in the field of an instantaneously cut-off extraneous current. A generalized statement of the problem has been found that guarantees the uniqueness of solution and its continuous dependence on the initial data under fairly sweeping assumptions about the conductivity and permeability of the body as well as the smoothness of boundaries of the body and the flaws. Possible generalizations are pointed out for the results to include ferromagnetic conducting bodies that are placed in the field of permanently switched-on current.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dyakin, V.V. and Sandovskii, V.A., Zadachi elektrodinamiki v nerazrushayushchem kontrole (Problems of Electrodynamics in Nondestructive Testing), Yekaterinburg: Inst. Phys. Met., Ural Branch, Russ. Acad. Sci., 2008.
Epov, M.I. and Morozova, G.M., TEM soundings in magnetic media, Russ. Geol. Geophys., 2010, vol. 51, no. 2, pp. 204–208.
Duvaut, G. and Lions, J.L., Inequalities in Mechanics and Physics, Berlin: Springer-Verlag, 1976.
Kalinin, A.V., Matematicheskie zadachi fizicheskoi diagnostiki. Korrektnost’ zadach elektromagnitnoi teorii v statsionarnom i kvazistatsionarnom priblizhenii (Mathematical Problems of Physical Testing. Well-Posedness of Problems of Electromagnetic Theory in Stationary and Quasistationary Approximations), Nizhny Novgorod: Nizhegorod. Gos. Univ., 2007.
Dyakin, V.V. and Marvin, S.V., Initial-boundary value problem and integrodifferential equations of electrodynamics for an inhomogeneous conductive body, Comput. Math. Math. Phys., 2008, vol. 48, no. 2, pp. 275–283.
Marvin, S.V. and Dyakin, V.V., Nonstationary boundary-value problem of electrodynamics for a nonmagnetic conducting sample, Elektrichestvo, 2008, no. 12, pp. 30–36.
Marvin, S.V. and Dyakin, V.V., A system of integro-differential equations of electrodynamics and the inverse Laplace transform, Russ. J. Nondestr. Test., 2008, vol. 44, no. 3, pp. 178–183.
Marvin, S.V., The existence and uniqueness of solution of initial-boundary value problem for the system of Maxwell equations for a nonferromagnetic flawed metal body, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Matem., 2016, no. 1, pp. 105–117.
Marvin, S.V., An initial-boundary value problem of structuroscopy of a nonferromagnetic metal solid with foreign dielectric inclusions using the residual field of an instantaneously cut-off extraneous current, Russ. J. Nondestr. Test., 2016, vol. 52, no. 2, pp. 85–94.
Gulyaev, B.B., Liteinye protsessy (Casting Processes), Moscow: Mashgiz, 1960.
Tamm, I.E., Osnovy teorii elektrichestva (Fundamentals of the Theory of Electricity), Moscow: Fizmatlit, 2003.
Richtmyer, R.D., Principles of Advanced Mathematical Physics, Berlin: Springer-Verlag, 1978.
Reed, M. and Simon, B., Methods of Modern Mathematical Physics, Vol. 2: Fourier Analysis, Self-Adjointness, New York: Academic, 1975.
Itô, K., Veroyatnostnye protsessy (Probability Processes), Moscow: Izd. Inost. Lit., 1963.
Krein, S.G., Linear Differential Equations in Banach Space, Providence: Am. Math. Soc., 1972.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.V. Marvin, 2016, published in Defektoskopiya, 2016, No. 11, pp. 27–38.
Rights and permissions
About this article
Cite this article
Marvin, S.V. Initial-boundary value problem of electromagnetic testing of a flawed ferromagnetic conductor by the residual field of an instantaneously cut-off current. Russ J Nondestruct Test 52, 638–646 (2016). https://doi.org/10.1134/S106183091611005X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106183091611005X