  Coefficient inverse problems related to identifying the right-hand side of an
equation with use of additional information is of interest among inverse
problems for partial differential equations. When considering non-stationary
problems, tasks of recovering the dependence of the right-hand side on time and
spatial variables can be treated as independent. These tasks relate to a class
of linear inverse problems, which sufficiently simplifies their study. This
work is devoted to a finding the dependence of right-hand side of
multidimensional parabolic equation on spatial variables using additional
observations of the solution at the final point of time - the final
overdetermination. More general problems are associated with some integral
observation of the solution on time - the integral overdetermination. The first
method of numerical solution of inverse problems is based on iterative solution
of boundary value problem for time derivative with non-local acceleration. The
second method is based on the known approach with iterative refinement of
desired dependence of the right-hand side on spacial variables. Capabilities of
proposed methods are illustrated by numerical examples for model
two-dimensional problem of identifying the right-hand side of a parabolic
equation. The standard finite-element approximation on space is used, the time
discretization is based on fully implicit two-level schemes.
