Stabilization of the Linear System of Magnetoelasticity

Thomas Duyckaerts

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Stabilization of the Linear System of Magnetoelasticity

Thomas Duyckaerts

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Abstract

We give a necessary and sufficient condition, of geometric type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is assumed. When the geometrical condition is not fulfilled, we show polynomial decay of the energy, for smooth initial conditions. Our strategy is to use micro-local defect measures to show suitable observability inequalities on high-frequency solutions of the Lame system.

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Thomas Duyckaerts. 2004-07-14. Stabilization of the Linear System of Magnetoelasticity. https://arxiv.org/abs/math/0407257

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