Communications in Mathematical Sciences

Volume 4 (2006)

Number 2

Relaxation approximation of some nonlinear Maxwell initial-boundary value problem

Pages: 331 – 344

DOI: http://dx.doi.org/10.4310/CMS.2006.v4.n2.a4

Authors

Gilles Carbou

Bernard Hanouzet

Abstract

Two nonlinear Maxwell systems are considered: Kerr model exhibiting an instantaneous response of the medium, Kerr-Debye model which contains some delay term and is a relaxation approximation of the first one. In one space dimension, we prove that the limit of the solution to the ingoing wave condition for Kerr-Debye model is a solution to the Kerr model.

2010 Mathematics Subject Classification

Primary 78A60. Secondary 35L50, 35L60, 35Q60, 78Mxx.

Full Text (PDF format)