An Inverse Problem for the Equation of Electrodynamics with Nonlinear Absorption

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 to the direct problem is obtained, and the existence and uniqueness theorems of solutions to the direct and inverse problems are proved.