Let \(\Omega\) be a region, occupied by a continuous medium and electromagnetic field within. The position vector in \(\Omega\) is denoted by \(\vec x\), and \(\vec n\) denotes the unit outward normal to \(\partial\Omega\). Physically, the boundary \(\partial \Omega\) is regarded as a conductor. For time-harmonic fields the conductor is modelled by letting the amplitudes \(\widetilde E_\tau\), \(\widetilde H_\tau\) of the tangential electrical field \(E_\tau\) and magnetic field \(H_\tau\) be related by \[ \widetilde E_\tau (\vec x,\omega)= \lambda (\vec x,\omega) \widetilde H_\tau (\vec x,\omega) \times\vec n (\vec x), \quad \vec x\in \partial\Omega \tag{1} \] where \(\lambda\) is an appropriate, possibly complex scalar and \(\omega\) is the angular frequency. The authors generalize (1) to time-dependent fields at dissipative boundaries and show that the generalization is of the form: \[ E_\tau(\vec x,t)= \eta_0 (\vec x)H_\tau (\vec x,t) x\vec n(\vec x)+ \int^\infty_0 \eta(\vec x,s) H^t_\tau(\vec x,s) \times n(\vec x)ds, \quad\vec x\in\partial\Omega. \tag{2} \] They also show that a general dissipative boundary condition results in the validity of the inequality \[ \int^d_0E_\tau(\vec x,t) \times H_\tau (\vec x,t)\cdot \vec n(\vec x)dt>0,\quad \vec x\in\partial \Omega \tag{3} \] for every nontrivial cycle on \([0,d)\), namely for every nonconstant time-dependent collection of state functions whose initial value (at \(t=0)\) and final value (at \(t=d)\) coincide. The authors prove that the dissipativity (3) of the boundary results in \[ \eta_0(\vec x)+ \int^\infty_0\eta (\vec x,s) \cos \omega st ds>0 \quad\forall\omega\in\mathbb{R}^+. \] They also investigate the initial-boundary-value problem for Maxwell's equations in material with linear law along with the boundary inequality (2) and prove the existence and uniqueness of the solution in \(\Omega\times (0,T)\), \(T0\).