Relaxation approximation of some nonlinear Maxwell initial-boundary value problem

Gilles Carbou (1) , Bernard Hanouzet (1)

1 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Initial boundary value problem; Kerr model; nonlinear Maxwell equation; Kerr-Debye model; relaxation; nonlinear Maxwell equation.

Domaines: Equations aux dérivées partielles [math.AP]

Gilles Carbou, Bernard Hanouzet. Relaxation approximation of some nonlinear Maxwell initial-boundary value problem. Communications in Mathematical Sciences, 2006, 4 (2), pp.331-344. ⟨hal-00196157⟩