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

Yakhno V.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.15, sa.1, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s00009-018-1065-4
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: 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 Üniversitesi Adresli: Evet

Özet

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.