Hyperbolicity of high-order systems of evolution equations

We study properties of evolution equations which are first order in time and arbitrary order in space (FTNS). Following Gundlach and Martin-Garcia (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.