Singular limits of quasi-linear hyperbolic systems in a bounded domain of R³ with applications to Maxwell’s equations

We establish a singular perturbation result for quasi-linear hyperbolic systems in a bounded domain of R³, depending on a small parameter. We prove and estimate the rate of convergence, as the parameter tends to zero, of uniformly stable solutions of the complete system to a solution of the reduced system. This result is then applied to the study of the convergence of the complete Maxwell equations to the quasi-stationary ones.