On the hyperbolicity of Maxwell's equations with a local constitutive law

Details On the hyperbolicity of Maxwell's equations with a local constitutive law On the hyperbolicity of Maxwell's equations with a local constitutive law

2010-11-11

arxiv.org/abs/1011.2536v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, no figures. Revised version contains 3 more references and several minor corrections. To appear in J. Math. Phys

Scientific paper

Maxwell's equations are considered in metric-free form, with a local but otherwise arbitrary constitutive law. After splitting Maxwell's equations into evolution equations and constraints, we derive the characteristic equation and we discuss its properties in detail. We present several results that are relevant for the question of whether the evolution equations are hyperbolic, strongly hyperbolic or symmmetric hyperbolic. In particular, we give a convenient characterisation of all constitutive laws for which the evolution equations are symmetric hyperbolic. The latter property is sufficient, but not necessary, for well-posedness of the initial-value problem. By way of example, we illustrate our results with the constitutive laws of biisotropic media and of Born-Infeld theory.

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