What question did this study set out to answer?

The research aims to determine unknown functions related to the absorption coefficient in electrodynamics.

April 3, 2026Journal of Applied and Industrial Mathematics0 citations

An Inverse Problem for the Equation of Electrodynamicswith Nonlinear Absorption

VRV. G. RomanovRussian Academy of Sciences TBT. V. BuguevaRussian Academy of Sciences

Key Points

The research aims to determine unknown functions related to the absorption coefficient in electrodynamics.
Considered the inverse problem of determining functions σ₀(x) and σ₁(x) in the absorption coefficient.
Obtained a priori estimates for solutions of the direct problem.
Proved existence and uniqueness theorems for solutions to both direct and inverse problems.
Established conditions under which solutions to the inverse problem are uniquely determined.
Showed that the estimated solutions align with existing theoretical frameworks.
Proved the existence of solutions to both direct and inverse problems under certain assumptions.

Abstract

The inverse problem of determining two unknown functions ₀ (x) and ₁ (x) included in the absorption coefficient (x, u) = ₀ (x) + ₁ (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.

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