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

Yakhno V.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.44, no.11, pp.9487-9506, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 11
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.7373
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.9487-9506
  • Keywords: analytical method, equations of elasticity, initial value problem, quasicrystals, symmetric hyperbolic system
  • Dokuz Eylül University Affiliated: Yes

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.