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September  2009, 25(3): 797-821. doi: 10.3934/dcds.2009.25.797

Energy decay rates of magnetoelastic waves in a bounded conductive medium

Ruy Coimbra Charão 1, , Jáuber Cavalcante Oliveira 1, and  Gustavo Alberto Perla Menzala 2,

1. 

Department of Mathematics, Federal University of Santa Catarina, CEP 88040-900, Florianópolis, SC, Brazil, Brazil
2. 

National Laboratory of Scientific Computation, LNCC/MCT, Av. Getulio Vargas 333, Quitandinha, Petrópolis, RJ, 25651-070, Brazil

Received  September 2008 Revised  June 2009 Published  August 2009

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: localized damping., magnetoelastic waves.
Mathematics Subject Classification: Primary: 35B40, 35Q60; Secondary: 35Q9.
Citation: Ruy Coimbra Charão, Jáuber Cavalcante Oliveira, Gustavo Alberto Perla Menzala. Energy decay rates of magnetoelastic waves in a bounded conductive medium. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 797-821. doi: 10.3934/dcds.2009.25.797
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