TY - JOUR

T1 - An Inverse Problem for Electrodynamics Equation with Nonlinear Quadratic Absorption

AU - Романов, Владимир Гаврилович

AU - Bugueva, T. V.

N1 - Romanov, V. G. An Inverse Problem for Electrodynamics Equation with Nonlinear Quadratic Absorption / V. G. Romanov, T. V. Bugueva // Siberian Advances in Mathematics. – 2025. – Vol. 35. - No. 4. – P. 305-323. – DOI 10.1134/S1055134425040030. – EDN HVSHQU. The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0009).

PY - 2025/12/22

Y1 - 2025/12/22

N2 - We consider an inverse problem on finding unknown functions σ0 and σ1 that occur in the formula σ(x, u2) = σ0 + σ1u2 for the absorption coefficient in electrodynamics equation. We obtain an a priori estimate for a solution to the direct problem and prove existence and uniqueness theorems for solutions to the direct and inverse problems.

AB - We consider an inverse problem on finding unknown functions σ0 and σ1 that occur in the formula σ(x, u2) = σ0 + σ1u2 for the absorption coefficient in electrodynamics equation. We obtain an a priori estimate for a solution to the direct problem and prove existence and uniqueness theorems for solutions to the direct and inverse problems.

KW - nonlinear equation

KW - electrodynamics

KW - inverse problem

KW - local existence

UR - https://www.scopus.com/pages/publications/105025426767

UR - https://elibrary.ru/item.asp?id=87368780

U2 - 10.1134/S1055134425040030

DO - 10.1134/S1055134425040030

M3 - Article

VL - 35

SP - 305

EP - 322

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 4

M1 - 3

ER -