Hyperbolicity of High Order Systems of Evolution Equations

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We study properties of evolution equations which are first order in time and arbitrary order in space (FTNS).

• Following Gundlach and Mart\'in-Garc\'ia (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.