Inverse problems for parabolic equations 2

Let $u_t-u_{xx}=h(t)$ in $0\leq x \leq \pi, t\geq 0.$ Assume that $u(0,t)=v(t)$, $u(\pi,t)=0$, and $u(x,0)=g(t)$. The problem is: {\it what extra data determine the three unknown functions $\{h, v, g\}$ uniquely?}. This question is answered and an analytical method for recovery of the above three functions is proposed.