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On the dissipative effect of a magnetic field in a Mindlin-Timoshenko plate model

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Abstract

In this paper we are concerned with a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. The magnetic field that permeates the plate consists of a non-stationary part and a uniform (constant) part. When the uniform magnetic field is aligned with the mid-plane of the plate, a strongly interactive system emerges with direct coupling between the elastic field and the magnetic field occurring in all the equations of the system. The unique solvability of the model is established within the framework of semigroup theory. Spectral analysis methods are used to show strong asymptotic stability and determine the polynomial decay rate of weak solutions.

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  1. School of Mathematics, University of the Witwatersrand, Private Bag X03, Braamfontein, Johannesburg, 2050, South Africa

    Marié Grobbelaar-Van Dalsen

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  1. Marié Grobbelaar-Van Dalsen
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Correspondence to Marié Grobbelaar-Van Dalsen.

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Grobbelaar-Van Dalsen, M. On the dissipative effect of a magnetic field in a Mindlin-Timoshenko plate model. Z. Angew. Math. Phys. 63, 1047–1065 (2012). https://doi.org/10.1007/s00033-012-0206-z

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