Existence, uniqueness, and error estimates for a model of polymer crystallization

We perform a mathematical analysis of a model for the crystallization of polymers. Essentially, the model is a system of both second order and first order evolutionary partial differential equations. The main novelty here is the fact that non-Lipschitz continuous functions of the unknown variables may appear in the constitutive equations. This lack of smoothness must be allowed in order for the model to account for the isokinetic assumption. Using monotonicty and $L^1$ techniques we prove existence and continuous dependence on the data of the weak solution to the mathematical problem. Moreover we introduce a time-discrete approximation to the problem, and we prove the convergence of the semidiscrete solutions to the continuous one, also giving optimal a priori error estimates.