  This paper is concerned with the inverse moving source problems for parabolic
equations. Given the temporal function, we prove the uniqueness of the
nonlinear inverse problem of determining the orbit function by final data
measured in a bounded domain. On the other hand, given the orbit function we
also show that the profile function can be uniquely determined by final data
measured in a bounded domain away from the domain enclosing the moving orbit.
The proofs adopt the Fourier approach and results from complex analysis.
