Initial value problem for the dynamic system of anisotropic elasticity

The main object of this paper is the Cauchy problem for the dynamic system of anisotropic elasticity. Existence and uniqueness theorems of weak and smooth solutions of this problem are established by the reduction of the original elasticity system into a symmetric hyperbolic system of the first order. The numerical method of the Cauchy problem solving for anisotropic elastic system with polynomial data is obtained and its correctness is established. The simulations of the numerical solutions are presented.