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 partial derivative(2)(t)u -Delta(x)u + q(t,x)u = 0 in Q = (0,T) x Omega with T > 0 and Omega a C-2 bounded domain of R-n, n >= 2, from partial observations of the solutions on partial derivative Q. More precisely, we look for observations on partial derivative Q that allows to recover uniquely a general time-dependent potential q without involving an important set of data. We prove global unique determination of q E L-infinity (Q) from partial observations on partial derivative Q. Besides being nonlinear, this problem is related to the inverse problem of determining a semilinear term appearing in a nonlinear hyperbolic equation from boundary measurements. (C) 2016 Elsevier Masson SAS. All rights reserved.