Determine whether the following statement is TRUE or FALSE.
Let $\varphi$, $\psi$ be twice continuously differentiable, non-zero functions defined on the interval
$[0, 1]$. Then the following initial boundary value problem
$u_{tt} - u_{xx} + u_t = 0$, $0 < x < 1$, $t > 0$,
$u(x, 0) = \varphi(x)$, $u_t(x, 0) = \psi(x)$, $0 \le x \le 1$,
$u(0, t) = 0$, $u(1, t) = 0$, $t \ge 0$
has at most one classical solution.
(A) FALSE.
(B) TRUE.
