On convergence rates of some iterative regularization methods for an inverse problem for a nonlinear parabolic equation connected with continuous casting of steel

In this paper we consider an inverse problem for a nonlinear one-dimensional heat equation, namely the problem of controlling the solidification front in a continuous cast steel slab, by appropriately choosing the cooling. We apply iterative regularization methods, especially Newton type methods and show their convergence with certain convergence rates under appropriate smoothness assumptions on the material parameters, the starting value of the iteration, and the solution of the inverse problem.