Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation

Pages: 547 - 558, Volume 2, Issue 3, September 2009      doi:10.3934/dcdss.2009.2.547

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Cleverson R. da Luz - Institute of Mathematics, Federal University of Rio de Janeiro, P.O. Box 68530, Rio de Janeiro, RJ, Brazil (email)
Gustavo Alberto Perla Menzala - National Laboratory of Scientific Computation, LNCC/MCT, Av. Getulio Vargas 333, Quitandinha, PetrĂ³polis, RJ, 25651-070, Brazil (email)

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.

Keywords:  Anisotropic Maxwell system, boundary dissipation, uniform stabilization.
Mathematics Subject Classification:  Primary: 35Q99, 35Q60, 35L99.

Received: July 2008;      Revised: March 2009;      Available Online: June 2009.