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When analysing the wave equation $u_{tt} = c^2 u_{xx}$ in my PDE's module, I understand the 'domain of dependence' which is where the value $u(x_0,t_0)$ is only depends on the initial value of $x$ (at $t=0$) in the closed interval $[x_0 - ct_0, x_0 + ct_0]$ and so it forms a triangle on the $x\, \, t$ plane.

Can someone please explain, intuitively, what the 'domain of influence' is? This is apparently the upside down triangle on the $x \, \, t$ plane starting at point $(x_0, 0)$?

Thanks!

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    As you said, you understand the "domain of dependence", then you can understand the "domain of influence" of point $P$ as the set $S$ of points in the $(x,t)$ plane such that for each $Q\in S$, $P$ is in the "domain of dependence" of $Q$.2012-05-03

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