Uniqueness of Solutions to the Helically Reduced Wave Equation with Sommerfeld Boundary Conditions

Authors

Charles G. Torre, Utah State UniversityFollow

Document Type

Article

Journal/Book Title/Conference

Journal of Mathematical Physics

Volume

47

Issue

7

Publisher

American Institute of Physics

Publication Date

2006

First Page

073501-1

Last Page

073501-7

Abstract

We consider the helical reduction of the wave equation with an arbitrary source on (n+1)-dimensional Minkowski space, n ≥ 2. The reduced equation is of mixed elliptic-hyperbolic type on Rn. We obtain a uniqueness theorem for solutions on a domain consisting of an n-dimensional ball B centered on the reduction of the axis of helical symmetry and satisfying ingoing or outgoing Sommerfeld conditions on ∂B ≈ Sn−1. Nonlinear generalizations of such boundary value problems (with n = 3) arise in the intermediate phase of binary inspiral in general relativity.

Comments

Originally published by the American Institute of Physics. Publisher's PDF and HTML fulltext available through the Journal of Mathematical Physics.

Recommended Citation

C.G. Torre, “Uniqueness of solutions to the helically reduced wave equation with Sommerfeld boundary conditions,” Journal of Mathematical Physics, vol. 47, 2006, p. 073501.

http://arxiv.org/abs/math-ph/0603073