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

被引：0

作者：

Mcintosh, Alan ^{[1
]}

Morris, Andrew J. ^{[2
]}

机构：

[1] Australian Natl Univ, Ctr Math & Its Applicat, Canberra, ACT 0200, Australia

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2013年 / 141卷 / 10期

基金：

澳大利亚研究理事会;

关键词：

Finite propagation speed; first order systems; C-0; groups; Huygens' principle; hyperbolic equations; SQUARE-ROOT PROBLEM; FUNCTIONAL CALCULI; COSINE FUNCTIONS; KATO;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：3515 / 3527

页数：13

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