Consider the initial value problem
$u_{tt}-c^{2}u_{xx}+\alpha u_{t}=0$ for $0<x<1$ and $t>0$
$u(0,t)=u(1,t)=0$ for $t>0$
$u(x,0)=g(x), u_{t}(x,0)=h(x)$ for $0<x<1$
where $c, \alpha>0$ are constants. use energy method to show that $C^{2}$ solution depends uniquely on $g$ and $h$.
