# Fundamental solution of wave equation

1. Jul 17, 2012

### sunrah

1. The problem statement, all variables and given/known data
show that
$E(x,t):= \frac{1}{2} \left\{ \begin{array}{ll} 1 & \mbox{if |x|<t };\\ 0 & \mbox{else}.\end{array} \right.$

is a fundamental solution of the wave equation.
2. Relevant equations
$LE = E_{tt} - \Delta E = \delta$

3. The attempt at a solution
firstly redefined $E:=\frac{1}{2}H(t-|x|)$

but the second order derivatives mean $LE:=\delta'(t-|x|)$