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Article
Uniqueness of Solutions to the Helically Reduced Wave Equation with Sommerfeld Boundary Conditions
Journal of Mathematical Physics
  • Charles G. Torre, Utah State University
Document Type
Article
Publisher
American Institute of Physics
Publication Date
1-1-2006
DOI
10.1063/1.2212667
Disciplines
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.
http://arxiv.org/abs/math-ph/0603073
Citation Information
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.