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To consider problems with parameters that change in time it needs to solve the time domain Maxwell's equations. If a medium is inhomogeneous than a problem becomes the initial and boundary value one. To solve such a problem it is convenient to transform the differential equations into integral equation, which contain initial and boundary conditions. This transformation can be done by virtue of the Green's function for the Maxwell equations. The advantages of the Maxwell equation Green's function over the Helmholtz and wave equation Green's functions are that it is a single compact expression governing radiation from any source. It is needed for a description of transient electromagnetic phenomena because such phenomena are characterized as a rule by 6D vector combining electric and magnetic fields. It is especially important for time-varying medium when constitutive laws connect these fields.

electromagnetic transients; integral equations in time domain; resolvent operator; time-varying medium