Focusing semilinear wave equation
= Focusing semilinear wave equation
{title2=$u_{tt}-\Delta u=u|u|^{p-1}$}
The focusing power <wave equation> is $u_{tt}-\Delta u=u|u|^{p-1}$. Its conserved <energy> has the negative potential term $-|u|^{p+1}/(p+1)$ and is not positive definite. <Localized ordinary differential equation blowup for a wave equation> produces smooth compactly supported data with finite maximal lifespan for suitable focusing powers.