The Well-Posedness of Dynamical Equations of Magneto-electro-elasticity

Yakhno V.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.15, no.1, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1007/s00009-018-1065-4
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Differential equations of magneto-electro-elasticity, coupling elastic and electromagnetic waves, symmetric hyperbolic system, existence, uniqueness, stability estimate theorems, MICROMECHANICAL ANALYSIS, PROPAGATION, SHELLS, PLATES, WAVES
  • Dokuz Eylül University Affiliated: Yes

Abstract

A mathematical model of wave propagation in magneto-electroelastic materials is obtained in the form of a symmetric hyperbolic system of the first-order partial differential equations. This model is a result of the qualitative analysis of the coupled time-dependent Maxwell's equations and equations of elastodynamics which are considered together with constitutive relations in non-homogeneous anisotropic magneto-electro-elastic materials. Applying the theory and methods of symmetric hyperbolic systems, we have proved that the reported model of wave propagation in magneto-electro-elastic materials satisfies the Hadamards correctness requirements: solvability, uniqueness and stability with respect to perturbation of data.