Relaxation approximation of the Kerr model for the three-dimensional initial-boundary value problem.
Langue
en
Article de revue
Ce document a été publié dans
Journal of Hyperbolic Differential Equations. 2009, vol. 6, n° 3, p. 577-614
World Scientific Publishing
Résumé en anglais
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. ...Lire la suite >
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.< Réduire
Mots clés en anglais
relaxation
nonlinear Maxwell equations
Initial-boundary value problem
Kerr model
Kerr-Debye model
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