Affiliation:
1. Institut de Mathématiques de Bordeaux, UMR 5251, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex, France
Abstract
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.
Publisher
World Scientific Pub Co Pte Lt
Subject
General Mathematics,Analysis
Cited by
6 articles.
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