On the large-time behavior of anisotropic Maxwell equations
Gustavo Perla Menzala, Cleverson Roberto da Luz · Differential and Integral Equations · 2009
Anisotropic Maxwell equations with electric conductivity are considered. Electromagnetic waves propagate in the exterior of a bounded connected obstacle with Lipschitz boundary. Our main result says that we can obtain uniform rates of decay of the total energy as $t \rightarrow + \infty$. No special requirements on the geometry of the obstacle are required. Previous results of this type were only given in the isotropic case. We use multipliers and properties of an associated evolution coupled system of first order.