On a mathematical model for the crystallization of polymers

Gualdani, Maria Pia

Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 1, pp. 161-179

Résumé

We consider a mathematical model proposed in [1] for the cristallization of polymers, describing the evolution of temperature, crystalline volume fraction, number and average size of crystals. The model includes a constraint $W_{eq}$ on the crystal volume fraction. Essentially, the model is a system of both second order and first order evolutionary partial differential equations with nonlinear terms which are Lipschitz continuous, as in [1], or Hölder continuous, as in [3]. The main novelty here is the fact that $W_{eq}$ is a function depending on the temperature T (which is actually the case). We analyse the model in two different conditions: for constitutive equations of non-Lipschitz type, we use monotonicity and $L^{1}$-technique to prove existence and continuous dependence on the data of a weak solution. For more regular constitutive equations, using a fixed point tecnique, we prove a global existence and uniqueness result for a classical solution.