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

McIntosh, Alan; Morris, Andrew J.

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

Date

2013

Authors

McIntosh, Alan

Morris, Andrew J.

Publisher

American Mathematical Society

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.