The research presented in this dissertation is carried out in two parts; the first, which is the main work of this dissertation, involves development of continuous differentiability of the solution with respect to the unknown parameters. For linear parabolic partial differential equations, only mild conditions are assumed on the admissible parameter space. The nonlinear partial differential equation we consider is a generalized Burgers’ equation, for which we establish the well-posedness and the smoothness properties of the solution with respect to the parameters.

In the second part, we consider parameter identification problems for these two parameter dependent systems. The identification scheme which we use here is the quasilinearization method. Based on the results in the first part of this work, we obtain existence and local convergence of the algorithm. We also present some numerical examples which demonstrate the performance of the quasilinearization scheme.