Abstract: We consider the system of Maxwell equations in which the current density depends nonlinearly on the electric field. In our case, the system is determined by four coefficients depending on the spatial variables. These coefficients are supposed to be compactly supported in a ball B(R) of radius R. For the electrodynamic equations, we pose a problem on a plane running wave with a sharp front incident on an inhomogeneity localized in the ball B(R). A formula for the calculation of the wave amplitude is derived. Further, we consider an inverse problem of finding the four coefficients determining the current from the wave front amplitude given for various directions of the incident plane wave on part of the boundary of B(R). We show that this inverse problem splits into four separate problems, one of which is the usual X-ray tomography problem and the other three are identical problems of integral geometry for a family of straight lines. These problems are studied, and a stability estimate for their solutions is found.

Cite: Romanov V.G.
An Inverse Problem for Electrodynamic Equations with a Nonlinear Dependence of the Current Density on the Electric Field
Differential Equations. 2025. V.61. N5. P.616-626. DOI: 10.1134/s0012266125050064 WOS Scopus

Original: Романов В.Г.
Обратная задача для уравнений электродинамики с нелинейной зависимостью силы тока от электрического напряжения
Дифференциальные уравнения. 2025. Т.61. №5. С.628-639. DOI: 10.31857/S0374064125050056 РИНЦ

Dates:

Submitted:	Mar 17, 2025
Accepted:	Mar 27, 2025
Published print:	May 15, 2025
Published online:	Sep 28, 2025

Identifiers:

Web of science:	WOS:001583417100003
Scopus:	2-s2.0-105017960941

Citing: Пока нет цитирований

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