Relaxation approximation of the Kerr model for the impedance initial-boundary value problem

Gilles Carbou; Bernard Hanouzet

doi:10.3934/proc.2007.2007.212

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2007, Volume 2007: 212-220. Doi: 10.3934/proc.2007.2007.212 open access

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Relaxation approximation of the Kerr model for the impedance initial-boundary value problem

Gilles Carbou^1, and
Bernard Hanouzet^2,

1.
MAB, UMR 5466, CNRS, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex
2.
Mathématiques Appliquées de Bordeaux, UMR 5466, CNRS, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex

Received: September 2006

Revised: January 2007

Published: September 2007

Abstract / Introduction Related Papers Cited by

Abstract

The Kerr-Debye model is a relaxation of the nonlinear Kerr model in which the relaxation coefficient is a finite response time of the nonlinear material. We establish the convergence of the Kerr-Debye model to the Kerr model when this relaxation coefficient tends to zero.

Keywords:

Nonlinear Maxwell Equation,
Relaxation.

Mathematics Subject Classification: 35L50, 35Q60.

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