Inverse Problems for Maxwell's Equations

Abstract

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)