  There is currently a great deal of interest in the 4D-Var data assimilation
scheme, in which one uses observational data to find the optimal initial
condition for a differential equation by minimizing a cost function over the
set of all possible initial states. For nonlinear models this cost function can
be nonconvex, and so the uniqueness of minimizers is not guaranteed. In this
paper we apply 4D-Var to Burgers' equation and prove that, once a sufficient
amount of data has been collected, there can be at most one physically
reasonable minimizer to the variational problem.
