domain of dependence

The interval of initial data that determines a wave solution's value at a single space-time point.

For the wave equation $u_{tt}=c^2u_{xx}$ , the domain of dependence of a point $(x_0,t_0)$ is the interval $[x_0-ct_0,\,x_0+ct_0]$ on the initial line $t=0$ -- by d'Alembert's formula, $u(x_0,t_0)$ depends on $f$ and $g$ only through their values on this interval, never on data outside it.