JournalspmVol. 68 , No. 4DOI 10.4171/pm/1898

Global existence of small solutions to the Kerr–Debye model for the three-dimensional Cauchy problem

  • Mohamed Kanso

    Université Bordeaux 1, Talence, France
Global existence of small solutions to the Kerr–Debye model for the three-dimensional Cauchy problem cover

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Abstract

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.