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

McIntosh, Alan; Morris, Andrew

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

Finite propagation speed for first order systems and Huygens’ principle for hyperbolic equations
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by Alan McIntosh and Andrew J. Morris

Proc. Amer. Math. Soc. 141 (2013), 3515-3527

DOI: https://doi.org/10.1090/S0002-9939-2013-11661-8

Published electronically: June 25, 2013

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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.

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