An inverse problem for nonlinear electrodynamic equations

Abstract An inverse problem for electrodynamic equations is considered. It is assumed that the electric current depends nonlinearly of the electric tension. This dependence is determined by seven finite functions of space variables. A direct problem for electrodynamic equations with a running plane wave going in direction ν from infinity is stated. Then traces of solutions of this direct problem on some bounded surface in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>ℝ</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> {\mathbb{R}^{3}} for different ν are used for posing an inverse problem. It is shown that the inverse problem is decomposed in seven separate problems. One of them is the X-ray tomography problem while 6 others are identical one to other integral geometry problems on a family of strait lines with a given weight function. The latter problems are studied and a stability estimate of solutions is found.