This article is cited in 1 paper

An inverse problem for the equation of electrodynamics with nonlinear absorption

V. G. Romanov^a, T.V. Bugueva<sup>ab

a</sup> Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
^b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia

Abstract: The inverse problem of determining two unknown functions $\sigma_0(x)$ and $\sigma_1(x)$ included in the absorption coefficient $\sigma(x,u)=\sigma_0(x)+\sigma_1(x)u$ in the equation of electrodynamics is considered. An a priori estimate of the solution of the direct problem is obtained, and the existence and uniqueness theorems of solutions to direct and inverse problems are proved.

Keywords: nonlinear equation, electrodynamics, inverse problem, local existence.

UDC: 517.958

Received: 07.03.2025
Revised: 06.06.2025
Accepted: 06.06.2025

DOI: 10.33048/SIBJIM.2025.28.205