Global existence of small solutions to the Kerr–Debye model for the three-dimensional Cauchy problem
Mohamed KansoUniversité Bordeaux 1, Talence, France
We consider the Kerr–Debye model, describing the electromagnetic wave propagation in a nonlinear medium exhibiting a finite response time. This model is quasilinear hyperbolic and endowed with a dissipative entropy. We consider the Cauchy problem in the three-dimensional case and show that, if the initial data are sufficiently small, the solutions are global in time.
Cite this article
Mohamed Kanso, Global existence of small solutions to the Kerr–Debye model for the three-dimensional Cauchy problem. Port. Math. 68 (2011), no. 4, pp. 389–409DOI 10.4171/PM/1898