Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation

Abstract

We consider the Maxwell system with variable anisotropic coefficients in a bounded domain Ω of 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.2000 Mathematics Subject Classification. Primary: 35Q99, 35Q60, 35L99.

Uniform decay rates of coupled anisotropic elastodynamic/Maxwell equations with nonlinear damping

“…C. R. Luz and G. P. Menzala [5] studied the asymptotic behavior of the anisotropic Maxwell equations with internal dissipation in exterior domains. In [6], the problem with boundary dissipation of Silver-Muller's type in bounded domains was treated. B. V. Kapitonov and G. P. Menzala [16] studied a transmission problem for a system of isotropic electromagneto-elasticity in a bounded domain.…”