Communications in Mathematical Sciences
Volume 4 (2006)
Relaxation approximation of some nonlinear Maxwell initial-boundary value problem
Pages: 331 – 344
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.