  In this paper, we consider an inverse problem for three dimensional
viscoelastic fluid flow equations, which arises from the motion of Kelvin-Voigt
fluids in bounded domains (a hyperbolic type problem). This inverse problem
aims to reconstruct the velocity and kernel of the memory term simultaneously,
from the measurement described as the integral over determination condition. By
using the contraction mapping principle in an appropriate space, a local in
time existence and uniqueness result for the inverse problem of Kelvin-Voigt
fluids are obtained. Furthermore, using similar arguments, a global in time
existence and uniqueness results for an inverse problem of Oseen type equations
are also achieved.
