An inverse source problem for Maxwell's equations in anisotropic media

Abstract

In this article, we consider nonstationary Maxwell's equations in an anisotropic medium in the (x 1, x 2, x 3)-space, where equations of the divergences of electric and magnetic flux densities are also unknown. Then we discuss an inverse problem of determining the x 3-independent components of the electric current density from observations on the plane x 3 = 0 over a time interval. Our main aim is, study conditional stability in the inverse problem provided the permittivity and the permeability are independent of x 3. The main tool is a new Carleman estimate.