Unique determination of a time-dependent potential for wave equations from partial data

We consider the inverse problem of determining a time-dependent potential $q$, appearing in the wave equation ${\mathrm{\partial }}_t^{2}u-\mathrm{\Delta }u+q(t,x)u=0$ in $Q=(0,T)\times \mathrm{\Omega }$ with $\mathrm{\Omega }$ a $C^2$ bounded domain of ${\mathbb{R}}^n$, $n\ge 2$, from partial observations of the solutions on $\mathrm{\partial }Q$. We prove global unique determination of a coefficient $q\in L^{\mathrm{\infty }}(Q)$ from these observations.