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

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

2006-03-28

arxiv.org/abs/math-ph/0603073v1

J.Math.Phys. 47 (2006) 073501

Physics

Mathematical Physics

Scientific paper

10.1063/1.2212667

We consider the helical reduction of the wave equation with an arbitrary source on $(n+1)$-dimensional Minkowski space, $n\geq2$. The reduced equation is of mixed elliptic-hyperbolic type on ${\bf R}^n$. 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 $\partial B\approx S^{n-1}$. Non-linear generalizations of such boundary value problems (with $n=3$) arise in the intermediate phase of binary inspiral in general relativity.

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