FINITE PROPAGATION SPEED FOR FIRST ORDER SYSTEMS AND HUYGENS' PRINCIPLE FOR HYPERBOLIC EQUATIONS

Authors/Editors

McIntosh, Abby

Research Areas

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Publication Details

Output type: Journal article

Author list: Mcintosh A, Morris AJ

Publisher: American Mathematical Society

Publication year: 2013

Journal: Proceedings of the American Mathematical Society (0002-9939)

Volume number: 141

Issue number: 10

Start page: 3515

End page: 3527

Number of pages: 13

ISSN: 0002-9939

eISSN: 1088-6826

Languages: English-Great Britain (EN-GB)

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-0 groups, Finite propagation speed, first order systems, Huygens' principle, hyperbolic equations

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