Finite Propagation Speed for First Order Systems and Huygens' Principle for Hyperbolic Equations

Details Finite Propagation Speed for First Order Systems and Huygens' Principle for Hyperbolic Equations Finite Propagation Speed for First Order Systems and Huygens' Principle for Hyperbolic Equations

2012-01-09

arxiv.org/abs/1201.1818v2

Mathematics

Analysis of PDEs

12 pages

Scientific paper

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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