Newton's principle for the wave equation (Q1311119)

A generalization of the classical Newton principle for the wave equation (1) \(({\partial^ 2 \over \partial t^ 2} - \Delta) u(x,t) = - f(x,t)\) is obtained. More specifically, given a source \(f(x,t)\) with support lying in a cylinder \(T = \{(x,t) \mid | x | \leq A\), \(t \geq 0\}\), a singular potential \(F(x,t)\) supported by \(\{x=0,\;t \geq 0\}\) is constructed such that the corresponding solutions of (1) coincide outside \(T\).