Time Dependent Inverse Source Problems for Integrodifferential Kelvin-Voigt System

In this work, time-dependent inverse source problems for an integrodifferential Kelvin-Voigt (Navier-Stokes-Voigt) system governing a flow of incompressible non-Newtonian fluids with viscoelastic properties is considered. The inverse problems considered consist of determining a time-dependent intensity of the density of external forces, along with the velocity field and the pressure of the fluids. The system is also supplemented with an initial and a boundary condition, and with two types of integral overdetermination conditions with respect to the space domain. Under suitable conditions on the data, the global-in-time existence and uniqueness of weak and strong solutions to the considered inverse problem were established.