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Nonlinear dynamic problems for 2D magnetoelastic waves

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Abstract

The propagation of magnetoelastic waves in a two-dimensional electroconductive elastic body is investigated. The waves are fully coupled through the nonlinear magnetoelastic effect. We prove the existence and uniqueness for both the forward problem and the inverse problem, which consists of identifying the unknown scalar time-dependent component in the body density force acting on the elastic body when some additional measurement is available.

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Acknowledgements

We are grateful to the LENEP/UENF and INCT-GP/CNPq/MEC, Brazil, for providing conditions to execute this work. The study was partly financed by the Coordination of Superior Level Staff Improvement (CAPES), Brazil.

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Authors and Affiliations

  1. Laboratory of Engineering and Exploration of Petroleum (LENEP), State University of Norte Fluminense Darcy Ribeiro (UENF), Av. Amaral Peixoto, km 163, Av. Brenand, s/n, Imboacica, Macaé, RJ, 27925-535, Brazil

    Viatcheslav Priimenko

  2. Laboratory of Mathematical Sciences (LCMAT), State University of Norte Fluminense Darcy Ribeiro (UENF), Av. Alberto Lamego, 2000, Parque Califórnia, Campos dos Goytacazes, RJ, 28013-602, Brazil

    Mikhail Vishnevskii

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  1. Viatcheslav Priimenko
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Correspondence to Viatcheslav Priimenko.

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Viatcheslav Priimenko is a member of the National Institute of Science and Technology of Petroleum Geophysics (INCT-GP/CNPq/MEC), Brazil.

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Priimenko, V., Vishnevskii, M. Nonlinear dynamic problems for 2D magnetoelastic waves. Nonlinear Differ. Equ. Appl. 30, 78 (2023). https://doi.org/10.1007/s00030-023-00887-3

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