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Mathematical Analysis for a Class of Partial Differential Equations with Dynamic Preisach Model

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Progress in Industrial Mathematics at ECMI 2018

Part of the book series: Mathematics in Industry ((TECMI,volume 30))

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Abstract

This work deals with the mathematical analysis and numerical solution of a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations. In this case, the values of the magnetic induction depend not only on the current values of the magnetic field, but also on the previous ones and on the velocity at which they have been attained. The hysteresis is modelled by the dynamic Preisach operator. Based upon the definition of dynamic relay, which is introduced and formalized as the solution of a multi-valued ordinary differential equation, the definition of the dynamic Preisach operator is recalled and some of their main properties established. Under suitable assumptions, the well-posedness of a weak formulation of the initial problem is shown and a numerical solution computed.

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References

  1. Bermúdez, A., Gómez, D., Venegas, P.: Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis. J. Comput. Appl. Math. 367, 112452 (2020). https://doi.org/10.1016/j.cam.2019.112452

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Acknowledgements

Work partially supported by Ministerio de Economía, Industria y Competitividad (MINECO), Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) under the research project MTM2017-86459-R, Xunta de Galicia (Spain) under grant 2017 GRC GI-1563 and by FONDECYT project 11160186 (Chile).

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Correspondence to Pablo Venegas .

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Bermúdez, A., Gómez, D., Venegas, P. (2019). Mathematical Analysis for a Class of Partial Differential Equations with Dynamic Preisach Model. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_44

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