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

Abstract

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.