| The electromagnetic waves propagation in a non linear medium can be described by the Kerr model in case of instantaneous response of the material, or by the Kerr-Debye model if the material exhibits a finite response time. Both models are quasilinear hyperbolic and are endowed with a dissipative entropy. Initial-boundary value problem with the maximal dissipative impedance boundary condition is considered. When the response time is fixed, in the one dimensional and the two dimensional transverse electric cases, the global existence of smooth solutions for the Kerr-Debye system is established. When the response time tends to zero, the convergence of the Kerr-Debye model to the Kerr model is proved in the general case: the Kerr model is the zero relaxation limit of the Kerr-Debye model |
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