A new method of solving equations of elasticity in inhomogeneous quasicrystals by means of symmetric hyperbolic systems

Hooke's law and dynamic equations of motion in inhomogeneous 3-D quaicrystals (QCs) were reduced to a symmetric hyperbolic system of the first-order partial differential equations. This symmetric hyperbolic system describes a new mathematical model of wave propagation in inhomogeneous 3-D QCs. Applying the theory and methods of symmetric hyperbolic systems, we have proved that this model satisfies the Hadamard's correctness requirements: solvability, uniqueness, and stability with respect to perturbation of data. Moreover, a new analytical method of solving the initial value problem for the obtained symmetric hyperbolic system which models wave propagation in vertical inhomogeneous quasicrystals was developed.