Geodesic
An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media
Applications of Mathematics, Tome 56 (2011) no. 3, pp. 315-339.

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The time-dependent system of partial differential equations of the second order describing the electric wave propagation in vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for solving an initial value problem for this system is the main object of the paper. This method consists in the following: the initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem is reduced to an operator integral equation. After that the operator integral equation is solved by the method of successive approximations. Finally, a solution of the original initial value problem is found by the inverse Fourier transform.
DOI : 10.1007/s10492-011-0019-y
Classification : 35A01, 35L15, 35L52, 35L55, 35Q60, 78A40
Keywords: equations of electromagnetic theory; hyperbolic system of second order partial differential equations; initial value problem; analytical method; Fourier transform 
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     title = {An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media},
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Yakhno, Valery; Sevimlican, Ali. An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media. Applications of Mathematics, Tome 56 (2011) no. 3, pp. 315-339. doi : 10.1007/s10492-011-0019-y. http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0019-y/

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