September  2009, 2(3): 547-558. doi: 10.3934/dcdss.2009.2.547

Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation

1. 

Institute of Mathematics, Federal University of Rio de Janeiro, P.O. Box 68530, Rio de Janeiro, RJ, Brazil

2. 

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

Received  July 2008 Revised  March 2009 Published  June 2009

We consider the Maxwell system with variable anisotropic coefficients in a bounded domain $\Omega$ of $\mathbb{R}^3$. The boundary conditions are of Silver-Muller's type. We proved that the total energy decays exponentially fast to zero as time approaches infinity. This result is well known in the case of isotropic coefficients. We make use of modified multipliers with the help of an elliptic problem and some technical assumptions on the permittivity and permeability matrices.
Citation: Cleverson R. da Luz, Gustavo Alberto Perla Menzala. Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 547-558. doi: 10.3934/dcdss.2009.2.547
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