Hyperbolicity of High Order Systems of Evolution Equations

Abstract

We study properties of evolution equations which are first order in time and arbitrary order in space (FTNS). Following Gundlach and Martín-García (2006) we define strong and symmetric hyperbolicity for FTNS systems and examine the relationship between these definitions, and the analogous concepts for first order systems. We demonstrate equivalence of the FTNS definition of strong hyperbolicity with the existence of a strongly hyperbolic first order reduction. We also demonstrate equivalence of the FTNS definition, up to N=4, of symmetric hyperbolicity with the existence of a symmetric hyperbolic first order reduction.

arXiv comment33 pages

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• Hyperbolicity of General Relativity in Bondi-like gauges
• Nonlinear Dynamics of Quadratic Gravity in Spherical Symmetry
• Gauge structure of the Einstein field equations in Bondi-like coordinates
• Hyperbolicity of Divergence Cleaning and Vector Potential Formulations of GRMHD
• Dual Foliation Formulations of General Relativity