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.
Existence, uniqueness, and error estimates for a model of polymer crystallization / Andreucci, Daniele; C., Verdi. - In: ADVANCES IN MATHEMATICAL SCIENCES AND APPLICATIONS. - ISSN 1343-4373. - STAMPA. - 5:(1995), pp. 391-409.
Existence, uniqueness, and error estimates for a model of polymer crystallization
ANDREUCCI, Daniele;
1995
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.