On Regularization of a Source Identification Problem in a Parabolic PDE and its Finite Dimensional Analysis

We consider the inverse problem of identifying a general source term,which is a function of both time variable and the spatial variable,in a parabolic PDE from the knowledge of boundary measurements of the solution on some portion of the lateral boundary.We transform this inverse problem into a problem of solving a compact linear operator equation.For the regularization of the operator equation with noisy data,we employ the standard Tikhonov regularization,and its finite dimensional realization is done using a discretization procedure involving the space L^(2)(0,τ;L^(2)(Ω)).For illustrating the specification of an a priori source condition,we have explicitly obtained the range space of the adjoint of the operator involved in the operator equation.