Determination of non-stationary potential analytical with respect to spatial variables

The inverse problem of determining coefficient before the lower term of the hyperbolic equation of the second order is considered. The coefficient depends on time and $n$ spatial variables. It is supposed that this coefficient is continuous with respect to variables $t, x$ and it is analytic in other spatial variables. The problem is reduced to the equivalent integro-differential equations with respect to unknown functions. To solve this equations the scale method of Banach spaces of analytic functions is applied. The local existence and global uniqueness results are proven. The stability estimate is also obtained.