  We study an inverse parabolic problem of identifying two source terms in heat
equation with dynamic boundary conditions from a final time overdetermination
data. Using a weak solution approach by Hasanov, the associated cost functional
is analyzed, especially a gradient formula of the functional is proved and
given in terms of the solution of an adjoint problem. Next, the existence and
uniqueness of a quasi-solution are also investigated. Finally, the numerical
reconstruction of some heat sources in a 1-D equation is presented to show the
efficiency of the proposed algorithm.
