  This work is concerned with the identification problem for what we call the
perturbation term or error term in a parabolic partial differential equation,
through its approximate periodic solutions. The observation is made over a
subregion of the physical domain. The existence and uniqueness problem of the
approximate periodic solutions is studied in the first part of the paper. A
solution to the identification problem is given in the second part of the
paper. The main ingredients to be used include the classical Garlerkin method
and the more recently developed Carleman estimates for a parabolic system.
