Finite Propagation Speed for First Order Systems and Huygens' Principle\n for Hyperbolic Equations

2012/01/09 by Alan McIntosh, McIntosh, Alan, Andrew J. Morris +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Applied mathematics #Computer science #Extension (predicate logic) #FOS: Mathematics #Huygens–Fresnel principle #Hyperbolic partial differential equation #Mathematical analysis #Mathematics #Metric (unit) #Order (exchange) #Partial differential equation #Physics #Pure mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.AP

paper · pdf · doi:10.48550/arxiv.1201.1818

12 pages

openalex publication_date 2012/01/09 · arxiv created 2012/01/25 · arxiv updated 2012/01/26 · openalex created_date 2022/10/01 · openalex updated_date 2026/08/05

Abstract

We prove that strongly continuous groups generated by first order systems on\nRiemannian manifolds have finite propagation speed. Our procedure provides a\nnew direct proof for self-adjoint systems, and allows an extension to operators\non metric measure spaces. As an application, we present a new approach to the\nweak Huygens' principle for second order hyperbolic equations.\n

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