Finite propagation speed for first order systems and Huygens' principle for hyperbolic equations

Alan Mcintosh; Andrew J. Morris

doi:10.1090/S0002-9939-2013-11661-8

Finite propagation speed for first order systems and Huygens' principle for hyperbolic equations

Alan Mcintosh, Andrew J. Morris

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	3515-3527
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-2013-11661-8
Publication status	Published - 2013

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title = "Finite propagation speed for first order systems and Huygens' principle for hyperbolic equations",

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

keywords = "C groups, Finite propagation speed, First order systems, Huygens' principle, Hyperbolic equations",

author = "Alan Mcintosh and Morris, \{Andrew J.\}",

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T1 - Finite propagation speed for first order systems and Huygens' principle for hyperbolic equations

AU - Mcintosh, Alan

AU - Morris, Andrew J.

PY - 2013

Y1 - 2013

N2 - We prove that strongly continuous groups generated by first order systems on Riemannian manifolds have finite propagation speed. Our procedure provides a new direct proof for self-adjoint systems and allows an extension to operators on metric measure spaces. As an application, we present a new approach to the weak Huygens' principle for second order hyperbolic equations.

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

KW - C groups

KW - Finite propagation speed

KW - First order systems

KW - Huygens' principle

KW - Hyperbolic equations

UR - https://www.scopus.com/pages/publications/84880728030

U2 - 10.1090/S0002-9939-2013-11661-8

DO - 10.1090/S0002-9939-2013-11661-8

M3 - Article

SN - 0002-9939

VL - 141

SP - 3515

EP - 3527

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 10

ER -

Finite propagation speed for first order systems and Huygens' principle for hyperbolic equations

Abstract

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