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 nonisothermal crystallization of polymers, which can be modeled by an initial-boundary value problem for a coupled system of parabolic and hyperbolic partial differential equations. The identification problem consists of 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 Frechet-differentiability of the parameter-to-output 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.