Stabilization and asymptotic behavior of dispersive medium models

We analyze the stability of different vectorial and scalar dispersive medium models set in a bounded domain of R d , d ≥ 1 . They correspond to the coupling between the Maxwell system (or the wave equation) and some first order differential equations of parabolic type. We show that some models have an exponential decay rate, while the other ones are only polynomially stable. In that last case we show that the obtained polynomial decay is optimal.