Mathematical problems of wave propagation in anisotropic media

This thesis is related with Initial Value Problem (IVP) and Initial Boundary Value Problem (IBVP) in a half space for the dynamic system of anisotropic elasticity. The existence and uniqueness theorems for IVP are established by using the tfıeory of symmetric hyperbolic sys-tems. An analytic method based on symbolic calculations for the construction of displacements for IVP is obtained. This method is extended for IBVP in a half space and it is proved that the obtained solution is a weak solution. The uniqueness of the solution for IBVP is also studied. Finally, the simulations of elastic wave propagations for both problems in different anisotropic crystals are obtained.