Mathematical models and methods of wave theory

In this thesis, initial value problems for theelectromagnetic system and system of elasticity are studied.Properties of solutions for considered initial value problems areproved. Using these properties analytic methods are suggested forproblems solving. These methods are based on symbolictransformations. As applications of these methods we construct thefundamental solutions for equations of anisotropic elasticity andderive electric fields, when the current density is presented in thepolynomial form. Robustness of the methods are confirmed bycomputational examples. Simulations of elastic and electric fieldsare obtained in different anisotropic materials.