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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.

Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation