带Sommerfeld边界条件的螺旋约化波动方程解的唯一性
Uniqueness of Solutions to the Helically Reduced Wave Equation with Sommerfeld Boundary Conditions
摘要：
本文考虑$(n+1)$维Minkowski空间$n\geq2$上具有任意源的波动方程的螺旋约化.约化方程是${\bf R}^n$上的混合椭圆-双曲型方程。我们得到了一个由$n$ -维球$B$组成的区域上的解的唯一性定理，该区域以螺旋对称轴的约化为中心，并满足$\partial B\approx S^{n-1}$上的进出Sommerfeld条件。在广义相对论中，这种边值问题的非线性推广（使用$n=3$）出现在双星螺旋的中间阶段。
英文摘要：
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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