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Article Dans Une Revue Journal of Hyperbolic Differential Equations Année : 2009

Relaxation approximation of the Kerr model for the three-dimensional initial-boundary value problem.

Résumé

The electromagnetic wave propagation in a nonlinear medium is described by the Kerr model in the case of an 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. The initial-boundary value problem with a maximal-dissipative impedance boundary condition is considered here. When the response time is fixed, in both the one-dimensional and 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 established in the general case, i.e. the Kerr model is the zero relaxation limit of the Kerr-Debye model.
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Dates et versions

hal-00992606 , version 1 (29-03-2019)

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Gilles Carbou, Bernard Hanouzet. Relaxation approximation of the Kerr model for the three-dimensional initial-boundary value problem.. Journal of Hyperbolic Differential Equations, 2009, 6 (3), pp.577-614. ⟨10.1142/S0219891609001939⟩. ⟨hal-00992606⟩

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