An inverse problem for an electrodynamics equation with nonlinear quadratic absorption

An inverse problem of determining two unknown functions $\sigma_0(x)$ and $\sigma_1(x)$ included in the absorption coefficient $\sigma(x,u^2)=\sigma_0+\sigma_1 u^2$ of an electrodynamics equation is considered. An a priori estimate for a solution of a direct problem is obtained, and existence and uniqueness theorems of solutions to the direct and an inverse problems are proved.

УДК 517.958

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