Iterative Regularization of a Parameter Identification Problem occurring in Polymer Crystallization

This paper is devoted to the mathematical analysis and regularization of an identification problem related to non-isothermal crystallization of polymers, which can be modelled by an initial-boundary value problem for a coupled system of parabolic and hyperbolic partial differential equations. The identification problem consists in estimating a material function of temperature, which appears as a nonlinearity in the equations. Existence and uniqueness of a solution of the direct problem is shown as well as its stability with respect to the parameter. Furthermore, we develop algorithms for the application of various iterative regularization methods to this particular problem. Their use is justified by verifying the Fr`echet-differentiability of the parameter-tooutput map, which is needed for their realization. The numerical performance of the iterative methods is compared with respect to speed of convergence, stability and efficiency. Keywords: Crystallization of Polymers, Iterative Reg..