TY - JOUR

T1 - On the hyperbolicity of Maxwell's equations with a local constitutive law.

AU - Perlick, Volker

PY - 2011

Y1 - 2011

N2 - 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 symmetric hyperbolic. In particular, we give a convenient characterization 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.

AB - 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 symmetric hyperbolic. In particular, we give a convenient characterization 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.

U2 - 10.1063/1.3579133

DO - 10.1063/1.3579133

M3 - Journal article

VL - 52

SP - 042903

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

ER -