Uniqueness of Solutions to the Helically Reduced Wave Equation with Sommerfeld Boundary ConditionsJournal of Mathematical Physics
PublisherAmerican Institute of Physics
AbstractWe 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.
Citation InformationC.G. Torre, “Uniqueness of solutions to the helically reduced wave equation with Sommerfeld boundary conditions,” Journal of Mathematical Physics, vol. 47, 2006, p. 073501.