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A new method of solving equations of elasticity in inhomogeneous quasicrystals by means of symmetric hyperbolic systems
Author(s) -
Yakhno Valery
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7373
Subject(s) - mathematics , hyperbolic partial differential equation , uniqueness , mathematical analysis , correctness , quasicrystal , elasticity (physics) , perturbation (astronomy) , hyperbolic function , partial differential equation , geometry , physics , thermodynamics , algorithm , quantum mechanics
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.