TY - JOUR

T1 - An Inverse Problem for the Equation of Electrodynamics with Nonlinear Absorption

AU - Романов, Владимир Гаврилович

AU - Бугуева, Татьяна Владимировна

N1 - Romanov, V.G., Bugueva, T.V. An Inverse Problem for the Equation of Electrodynamics with Nonlinear Absorption. J. Appl. Ind. Math. 19, 322–347 (2025). The work was carried out within the framework of the state assignment of the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (project FWNF-2022-0009).

PY - 2025/6

Y1 - 2025/6

N2 - The inverse problem of determining two unknown functions σ0(x) and σ1(x) included in the absorption coefficient σ(x,u) = σ0(x) + σ1(x)u in the equation of electrodynamics is considered. An a priori estimate of the solution to the direct problem is obtained, and the existence and uniqueness theorems of solutions to the direct and inverse problems are proved.

AB - The inverse problem of determining two unknown functions σ0(x) and σ1(x) included in the absorption coefficient σ(x,u) = σ0(x) + σ1(x)u in the equation of electrodynamics is considered. An a priori estimate of the solution to the direct problem is obtained, and the existence and uniqueness theorems of solutions to the direct and inverse problems are proved.

KW - nonlinear equation

KW - electrodynamics

KW - inverse problem

KW - local existence

UR - https://www.scopus.com/pages/publications/105035384442

U2 - 10.1134/S1990478925020115

DO - 10.1134/S1990478925020115

M3 - Article

VL - 19

SP - 322

EP - 347

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -