Inverse Problems for Maxwell's Equations

Part 1 Cauchy problem for Maxwell's equations: Maxwell's equations as a hyperbolic symmetric system; structure of the Cauchy problem solution in case of the current located on the media interface. Part 2 One-dimensional inverse problems: structure of the Fourier-image of the Cauchy problem solution for one-dimensional medium in case of the current located at a point; the problem of determining the medium permittivity; the problem of determining the conductivity co-efficient; the problem of determining all the co-efficients of Maxwell's equations. Part 3 Multi-dimensional inverse problems: linearization method applied to the inverse problems; investigation of the linearized problem of determining the permittivity co-efficient; unique solvability theorem for a two-dimensional problem of determining the conductivity co-efficient analytic in one variable; on the uniqueness of the solution of three-dimensional inverse problems. Part 4 Inverse problems in the case of source periodic in time: one-dimensional inverse problems; linear one-dimensional inverse problem; linearized three-dimensional inverse problems. Part 5 Inverse problems for quasi-stationary Maxwell's equations: on correspondence between the solutions of quasi-stationary and wave Maxwell's equations; a one-dimensional inverse problem of determining the conductivity and permeability co-efficients; the one-dimensional inverse problem for wave-quasi-stationary system of equations. Part 6 The inverse problems for the simplest anisotropic media: on the uniqueness of determination of permittivity and permeability in anisotropic media; on the problem of determining permittivity and conductivity tensors. Part 7 Numerical methods. Part 8 Convergence results. Part 9 Examples (Part contents)