= Localized ordinary differential equation blowup for a wave equation
A spatially constant blowup profile for a <wave equation> solves an <ordinary differential equation>. Choose smooth compactly supported initial data which agree with the profile on a ball larger than its blowup time times the <wave speed>. <Finite propagation speed> preserves agreement in an interior <light cone>, forcing finite-time breakdown of the localized solution. For $u_{tt}-\Delta u=u^3$, the profile $u(t)=\sqrt2/(1-t)$ is one example.
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