Publication at Faculty of Mathematics and Physics |
2008
Abstract
We report on very recent developments concerning the modelling of the complex behaviour of materials within the framework of implicit constitutive theory due to K.~R.~Rajagopal. In this paper, we restrict ourselves to a hierarchy of power-law-like fluids.
For such a class of fluids, we provide an overview of recent results concerning the mathematical analysis of the relevant boundary value problems. Mathematical results are presented for the (Rothe) time discretizations of evolutionary problems.
The main purpose of this paper is to emphasize the mathematical tools involved in the theoretical analysis and to initiate the development of the numerical methods for the problems presented here.