= Exponential initial-velocity tail for the Klein-Gordon equation
{title2=$u(x,t)=te^{-|x|}\quad(|x|>t)$}
For $u_{tt}=u_{xx}-u$ with $u(x,0)=0$ and $u_t(x,0)=e^{-|x|}$, the solution outside $|x|\leq t$ is exactly $te^{-|x|}$. On the positive half-line, $te^{-x}$ satisfies both the equation and initial data; the <finite propagation speed> limits dependence at $x>t$ to positive initial points. Uniqueness on this <domain of dependence> proves the formula there, and reflection gives the negative half-line. The exterior tail is nonzero because the initial velocity is not compactly supported.
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