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

A mathematical model of wave propagation in magneto-electro-elastic 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.