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


Authors: Alan McIntosh and Andrew J. Morris
Journal: Proc. Amer. Math. Soc. 141 (2013), 3515-3527
MSC (2010): Primary 35F35, 35L20; Secondary 47D06
DOI: https://doi.org/10.1090/S0002-9939-2013-11661-8
Published electronically: June 25, 2013
MathSciNet review: 3080173
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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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Additional Information

Alan McIntosh
Affiliation: Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia
Email: alan.mcintosh@anu.edu.au

Andrew J. Morris
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Address at time of publication: Mathematical Institute, University of Oxford, Oxford, OX1 3LB, United Kingdom
Email: morrisaj@missouri.edu, andrew.morris@maths.ox.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2013-11661-8
Keywords: Finite propagation speed, first order systems, $C_0$ groups, Huygens' principle, hyperbolic equations.
Received by editor(s): December 24, 2011
Published electronically: June 25, 2013
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.