On some classes of inverse problems on determining source functions for heat and mass transfer systems

In this paper, we considers the question on the well-posedness in Sobolev spaces of the problem of determining the source function in a heat and mass transfer system consisting of the Navier–Stokes system, a parabolic equation for temperature, and a parabolic system for the concentrations of substances being transferred. Weighted integrals solution over the spatial domain serve as overdetermination conditions. A local (in time) existence theorem for the solution of the problem in the nonlinear case is proved and stability estimates are obtained; for a linearized system, a global existence theorem is obtained.