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Exponential stabilization of magnetoelastic waves in a Mindlin–Timoshenko plate by localized internal damping

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Abstract

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047–1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin–Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function \({{{\mathbf{p}}}({\mathbf{x}},{\mathbf{U}}_t)}\), that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin–Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.

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  1. School of Mathematics, Private Bag X03, Wits, 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. Exponential stabilization of magnetoelastic waves in a Mindlin–Timoshenko plate by localized internal damping. Z. Angew. Math. Phys. 66, 1751–1776 (2015). https://doi.org/10.1007/s00033-015-0507-0

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  • DOI: https://doi.org/10.1007/s00033-015-0507-0

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