Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation

Cleverson R. da Luz; Gustavo Alberto Perla Menzala

doi:10.3934/dcdss.2009.2.547

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2009, Volume 2, Issue 3: 547-558. Doi: 10.3934/dcdss.2009.2.547

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Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation

Cleverson R. da Luz^1, and
Gustavo Alberto Perla Menzala^2,

1.
Institute of Mathematics, Federal University of Rio de Janeiro, P.O. Box 68530, Rio de Janeiro, RJ
2.
National Laboratory of Scientific Computation, LNCC/MCT, Av. Getulio Vargas 333, Quitandinha, Petrópolis, RJ, 25651-070

Received: July 2008

Revised: March 2009

Published: September 2009

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: Primary: 35Q99, 35Q60, 35L99.

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