Maxwell´s equations for bi-anisotropic materials as a symmetric hyperbolic system: Theory and computer application

This paper considers inhomogeneous non-dispersive bi-anisotropic materials characterized by matrices of electric permittivity, magnetic permeability and magnetoelectric characteristics. The time dependent Maxwell´s equations together with zero initial data are analyzed and an initial value problem (IVP) is formulated. This IVP is reduced to the IVP for a symmetric hyperbolic system of partial differential equations of the first order. Applying the theory of symmetric hyperbolic systems new results related to existence, uniqueness, and stability estimate have been obtained for the IVP of Maxwell´s equations in inhomogeneous bi-anisotropic materials. A new formula for the solution of the IVP has been derived for homogeneous bi-anisotropic materials. Using this formula the computation of the electric and magnetic fields has been made.