An initial boundary value problem for a singularly perturbed integro-differential parabolic equation with a source is considered. The inverse problem of determining the time evolution of the source from additional information about the solution of the equation is formulated. Approximate solutions of the inverse problem are constructed by expanding the solution of the initial boundary value problem in a small parameter. Accuracy estimates for the approximate solutions are proved.
A. M. Denisov (Thu,) studied this question.