The wave equation is given as below: $$ u_{tt}−u_{xx}= 0$$
$$ u(x, 0) = \begin{cases} 1 - (x+3)^2 & (-4 < x < -2) \\ 8 - 2(x-4)^2 & (2 < x < 6) \\ 0 & (x \leq -4, -2 \leq x \leq 2, x \geq 6) \end{cases} \ u_t(x, 0) = 0 $$
Find the value of $u(0,2)$, $u(0,3)$, $u(0,8)$
Since $-2 < 0 < 2$, the value should be $0$, but actually it's not. Why?