Global logarithmic stability in inverse hyperbolic problem by arbitrary boundary observation

We study the global stability in determination of a coefficient of the zerothorder term in a second-order hyperbolic equation from data of the solution in a subboundary over a time interval. Providing regular initial data, without any assumption on the dynamics (i.e. without the geometric optics condition for the observability), we prove the uniqueness in multidimensional hyperbolic inverse problems with a single measurement. Moreover, we show that our uniqueness results yield the logarithm stability estimate in L(2) space for solution of the inverse problem under consideration.