A generalized solution of the cauchy problem for anisotropic electrodynamic system

Initial valve problems for some hiperbolic equations and Maxwell's system were reduced to the integral equations of Volterra type with the operator kernels in this thesis. The method of the successive approximations for finding solutions of these integral equations was successfuly applied. As result the existence and uniqueness theorems were proved for the considered initial valve problems. Constructing fundamental solutions of the Cauchy problem for hyperbolic equations and system is a very important problem because by means of these fundamental solutions we find solutions of the Cauchy problems for equations and systems with arbitrary nonhomogeneous terms and initial data. Basic features of the structure of the fundamental solutions for hyperbolic equations are well known.