All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Journal of Mathematical Physics

Volume

44

Issue

12

Publisher

American Institute of Physics

Publication Date

2003

First Page

6223

Last Page

6232

DOI

10.1063/1.1623930

Abstract

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.

Comments

Originally published by the American Institute of Physics. Publisher's PDF can be accessed through the Journal of Mathematical Physics.

http://arxiv.org/abs/math-ph/0309008