Energy decay rates for solutions of Maxwell’s system with a memory boundary condition

We consider the stabilization of Maxwell’s equations with space variable coefficients in a bounded region with a smooth boundary, subject to dissipative boundary conditions of memory type on the boundary. Under suitable conditions on the domain and on the permeability and permittivity coefficients, we prove the exponential/polynomial decay of the energy. Our result is mainly based
on the use of the multipliers method and the introduction of a suitable Lyapounov functional.