2014/12/18 by David Hilditch, Ronny Richter · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Applied mathematics #Computer science #Equivalence (formal languages) #First order #Geometry #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Order (exchange) #Pure mathematics #Reduction (mathematics) #Space (punctuation) #gr-qc #math.AP
paper · pdf · doi:10.1142/s0219891615500010
published as JHDE Volume 12, Issue 1 (2015) · 33 pages
arxiv created 2014/12/18 · openalex publication_date 2015/03/01 · arxiv updated 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.