On determining the source function in heat and mass transfer problems under integral overdetermination conditions

We examine an inverse problem of determining the right-hand side (source function) in a parabolic equation from integral overdetermination data. By a solution to a parabolic equation we mean a weak solution, and the right-hand side in this equation can be a distribution of a certain class. Under some conditions on the data of the problem, we demonstrate that this inverse problem is well-posed and, in particular, stability estimates hold.