AN INVERSE PROBLEM FOR ELECTRODYNAMIC EQUATIONS WITH A NONLINEAR CONDUCTIVITY

Abstract

An inverse problem of determination of a variable coefficient in electrodynamic equations with a nonlinear conductivity is considered. It is supposed that the unknown coefficient is a smooth function of space variables and finite in \({{\mathbb{R}}^{3}}\). From a homogeneous space a plane wave going in a direction fall down on a heterogeneousness. The direction is a parameter of the problem. The module of the electrical strength vector for some diapason of directions and for moments of the time close to arriving the wave at points of a surface of a ball, inside of which the heterogeneousness is contained, is given as the information for solution of the inverse problem. It is shown that this information reduces the inverse problem to the well known X-ray tomography. Algorithms of the numerical solution of the later problem is well developed.