range (domain) of influence

The set of future space-time points a single piece of initial data at one location can possibly affect.

For the wave equation $u_{tt}=c^2u_{xx}$ , the range of influence of a point $x_0$ on the initial line is the wedge $\{(x,t): |x-x_0|\le ct,\ t\ge0\}$ -- the complementary statement to the domain of dependence: $(x,t)$ can be affected by data at $x_0$ exactly when $(x_0,0)$ lies in $(x,t)$ 's own domain of dependence.