BSU Bulletin. Mathematics, Informatics
Bibliographic description:
INITIAL BOUNDARY VALUE PROBLEM OF ELECTRODYNAMICS FOR A DEFECTIVE FERRITE BODY // BSU Bulletin. Mathematics, Informatics. - 2019. №1. . - С. 31-40.
Title:
INITIAL BOUNDARY VALUE PROBLEM OF ELECTRODYNAMICS FOR A DEFECTIVE FERRITE BODY
Financing:
Codes:
Annotation:
The article considers initial boundary value problem for Maxwell's equations in re- lation to a ferrite body, which has some structural defects. For initial boundary value problem we have chosen a functional class that takes into account the matching conditions on the interface of two media, which are not perfect conductors. Vector fields of this functional class are square-integrable in the whole space and have square-integrable generalized rotors. In addition, vector fields are time- differentiable in the sense of convergence in mean-square norm. Operating with broad assumptions about the dependence of electrical conductivity, dielectric and magnetic permeability of a ferrite on spaces coordinates, and natural assumptions about the dependence of external current on time, it has been shown, that in the given functional class there is one and only one solution of the considered initial boundary value problem, and that solution is continuous in the initial conditions.
Keywords:
Maxwell’s equations; initial conditions; matching conditions; mean- square norm; Banach space; existence theorem; generalized rotor; integro- differential equations; closed operator; inverse operator.
List of references:
Dyakin V. V., Sandovskii V. A. Zadachi elektrodinamiki v nerazrushayushchem kontrole [Problems of Electrodynamics in Nondestructive Testing]. Ekaterinburg: IMP UB RAS Publ., 2008. 390 p.
Duvant G., Lions J. L. Inequalities in Mechanics and Physics. Springer-Verlag Berlin Heidelberg, 1976. 384 p.
Kalinin A. V. Matematicheskie zadachi fizicheskoi diagnostiki. Korrektnost zad- ach elektromagnitnoi teorii v statsionarnom i kvazistatsionarnom priblizhenii [Mathe- matical Problems of Physical Diagnostics. The Correctness of Electromagnetic Theory Problems in Steady-State and Quasi-Steady-State Approximation]. Nizhnii Novgorod: Nizhny Novgorod State University Publ., 2007. 121 p.
Marvin S. V. Nachalno-kraevaya zadacha elektromagnitnogo kontrolya de- fektnogo ferromagnitnogo provodnika ostatochnym polem mgnovenno vyklyu- chennogo storonnego toka [Initial Boundary Value Problem of Electromagnetic Con- trol of a Defect Ferromagnetic Conductor by the Residual Field of an Instantaneous Switched-Off Extrinsic Current]. Russian Journal of Nondestructive Testing. 2016. No. 11. Pp. 27–38. DOI: 10.1134/S106183091611005X.
Marvin S. V. Nachalno-kraevaya zadacha dlya odnorodnoi sistemy uravnenii Maksvella v sluchae magnitodielektricheskogo tela s provodyashchimi ferromagnit- nymi vklyucheniyami [Initial Boundary Value Problem for a Homogeneous System of Maxwell’s Equations in the Case of a Magnetodielectric Body with Conducting Ferro- magnetic Inclusions]. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika. 2017. No. 47. Pp. 22–36. DOI: 10.17223/19988621/47/3.
Ilinskii A. S., Kravtsov V. V., Sveshnikov A. G. Matematicheskie modeli elek- trodinamiki [Mathematical Models of Electrodynamics]. Moscow: Vysshaya shkola, 1991. 224 p.
Krein S. G. Lineinye differentsialnye uravneniya v banakhovom prostranstve
[Linear Differential Equations in a Banach Space]. Moscow: Nauka Publ., 1967. 464 p.
Duvant G., Lions J. L. Inequalities in Mechanics and Physics. Springer-Verlag Berlin Heidelberg, 1976. 384 p.
Kalinin A. V. Matematicheskie zadachi fizicheskoi diagnostiki. Korrektnost zad- ach elektromagnitnoi teorii v statsionarnom i kvazistatsionarnom priblizhenii [Mathe- matical Problems of Physical Diagnostics. The Correctness of Electromagnetic Theory Problems in Steady-State and Quasi-Steady-State Approximation]. Nizhnii Novgorod: Nizhny Novgorod State University Publ., 2007. 121 p.
Marvin S. V. Nachalno-kraevaya zadacha elektromagnitnogo kontrolya de- fektnogo ferromagnitnogo provodnika ostatochnym polem mgnovenno vyklyu- chennogo storonnego toka [Initial Boundary Value Problem of Electromagnetic Con- trol of a Defect Ferromagnetic Conductor by the Residual Field of an Instantaneous Switched-Off Extrinsic Current]. Russian Journal of Nondestructive Testing. 2016. No. 11. Pp. 27–38. DOI: 10.1134/S106183091611005X.
Marvin S. V. Nachalno-kraevaya zadacha dlya odnorodnoi sistemy uravnenii Maksvella v sluchae magnitodielektricheskogo tela s provodyashchimi ferromagnit- nymi vklyucheniyami [Initial Boundary Value Problem for a Homogeneous System of Maxwell’s Equations in the Case of a Magnetodielectric Body with Conducting Ferro- magnetic Inclusions]. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika. 2017. No. 47. Pp. 22–36. DOI: 10.17223/19988621/47/3.
Ilinskii A. S., Kravtsov V. V., Sveshnikov A. G. Matematicheskie modeli elek- trodinamiki [Mathematical Models of Electrodynamics]. Moscow: Vysshaya shkola, 1991. 224 p.
Krein S. G. Lineinye differentsialnye uravneniya v banakhovom prostranstve
[Linear Differential Equations in a Banach Space]. Moscow: Nauka Publ., 1967. 464 p.
Article.pdf