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

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Abstract

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.

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Authors and Affiliations

  1. Electrical and Electronics Engineering Department, Dokuz Eylul University, Izmir, Turkey

    Valery Yakhno

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  1. Valery Yakhno
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Correspondence to Valery Yakhno.

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Yakhno, V. The Well-Posedness of Dynamical Equations of Magneto-electro-elasticity. Mediterr. J. Math. 15, 21 (2018). https://doi.org/10.1007/s00009-018-1065-4

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  • DOI: https://doi.org/10.1007/s00009-018-1065-4

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