A new method of solving equations of elasticity in inhomogeneous quasicrystals by means of symmetric hyperbolic systems. (6th April 2021)

• Record Type: Journal Article
• Authors: Yakhno, Valery
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 11(2021)
• Page Start: 9487
• Page End: 9506
• Publication Date: 2021-04-06
• Subjects: analytical method -- equations of elasticity -- initial value problem -- quasicrystals -- symmetric hyperbolic system; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7373
• Languages: English
• ISSNs: 0170-4214

Abstract

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.