Energy decay rates of magnetoelastic waves in a bounded conductive medium

Ruy Coimbra Charão; Jáuber Cavalcante Oliveira; Gustavo Alberto Perla Menzala

doi:10.3934/dcds.2009.25.797

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2009, Volume 25, Issue 3: 797-821. Doi: 10.3934/dcds.2009.25.797

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Energy decay rates of magnetoelastic waves in a bounded conductive medium

1.
Department of Mathematics, Federal University of Santa Catarina, CEP 88040-900, Florianópolis, SC
2.
National Laboratory of Scientific Computation, LNCC/MCT, Av. Getulio Vargas 333, Quitandinha, Petrópolis, RJ, 25651-070

Received: August 31, 2008

Revised: May 31, 2009

Published: August 2009

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Abstract

We consider a coupled system of evolution equations modeling the propagation of elastic waves interacting with a magnetic field in a bounded simply connected region of $\mathbb{R}^3$ with boundary of class $C^2$. A nonlinear dissipative mechanism is allowed to be effective in an small subregion of $\Omega$. We prove that the total energy decays as $t \to +\infty$.

Keywords:

magnetoelastic waves,
localized damping.

Mathematics Subject Classification: Primary: 35B40, 35Q60; Secondary: 35Q99.

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