Strong stabilization of a structural acoustic model,which incorporates shear and thermal effects in the structural component |
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Authors: | Marié Grobbelaar‐Van Dalsen |
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Institution: | School of Mathematics, University of the Witwatersrand, Private Bag X03, 2050 WITS, South Africa |
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Abstract: | In this paper we consider the question of stabilization of a linear three‐dimensional structural acoustic model, which incorporates displacement, rotational inertia, shear and thermal effects in the flat flexible structural component of the model. We show strong stabilization of the coupled model without incorporating viscous or boundary damping in the equations for the gas dynamics and without imposing geometric conditions. It turns out that damping is needed in the interior of the plate. Our main tool is an abstract resolvent criterion due to Y. Tomilov. Copyright © 2009 John Wiley & Sons, Ltd. |
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Keywords: | structural acoustic model interactive strong stability resolvent criterion |
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