Solvability of some inverse problems for the nonstationary heat-and-mass-transfer system

We study solvability of inverse problems of finding the right-hand side together with a solution itself for the nonstationary heat-and-mass-transfer system. The system consists of the Navier–Stokes system whose right-hand side contains the temperature of a fluid and the concentration of an admixture and the parabolic equations for the temperature of a fluid and the concentration. The right-hand side of the equation for the concentration is unknown and characterizes the volumetric density of sources of an admixture in a fluid. The usual boundary conditions are supplemented with the overdetermination conditions which are the values of the concentration on some system of surfaces.