= Support widening for the wave equation
{title2=$\operatorname{supp}u(\cdot,t)\subseteq[-a-ct,a+ct]$}
For whole-line <Cauchy data> with <support> contained in $[-a,a]$, the displayed inclusion holds at $t\geq0$. A short check uses <D'Alembert's formula>: if $x>a+ct$, both sampled endpoints and the whole <interval> of <integration> lie to the right of $a$, so all contributions vanish; the argument for $x<-a-ct$ is identical. The inclusion can be strict, and a nonzero response at the first permitted arrival is not guaranteed.
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