The Helically-Reduced Wave Equation as a Symmetric-Positive System

Details The Helically-Reduced Wave Equation as a Symmetric-Positive System The Helically-Reduced Wave Equation as a Symmetric-Positive System

2003-09-02

arxiv.org/abs/math-ph/0309008v1

J.Math.Phys. 44 (2003) 6223-6232

Physics

Mathematical Physics

18 pages, plain TeX, to appear in Journal of Mathematical Physics

Scientific paper

Motivated by the partial differential equations of mixed type that arise in the reduction of the Einstein equations by a helical Killing vector field, we consider a boundary value problem for the helically-reduced wave equation with an arbitrary source in 2+1 dimensional Minkowski spacetime. The reduced equation is a second-order partial differential equation which is elliptic inside a disk and hyperbolic outside the disk. We show that the reduced equation can be cast into symmetric-positive form. Using results from the theory of symmetric-positive differential equations, we show that this form of the helically-reduced wave equation admits unique, strong solutions for a class of boundary conditions which include Sommerfeld conditions at the outer boundary.

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