Relaxation approximation of some nonlinear Maxwell initial-boundary value problem

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.

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Published 1 January 2006