  This work investigates an inverse problem of determining the radiative
coefficient in a degenerate parabolic equation from the final overspecified
data. Being different from other inverse coefficient problems in which the
principle coefficients are assumed to be strictly positive definite, the
mathematical model discussed in the paper belongs to the second order parabolic
equations with non-negative characteristic form, namely that there exists
degeneracy on the lateral boundaries of the domain. The uniqueness of the
solution is obtained by the contraction mapping principle. Based on the optimal
control framework, the problem is transformed into an optimization problem and
the existence of the minimizer is established. After the necessary conditions
which must be satisfied by the minimizer are deduced, the uniqueness and
stability of the minimizer are proved. By minor modification of the cost
functional and some \emph{a-priori} regularity conditions imposed on the
forward operator, the convergence of the minimizer for the noisy input data is
obtained in the paper. The results obtained in the paper are interesting and
useful, and can be extended to more general degenerate parabolic equations.
