Since the early 1960s, the mathematical theory of variational
inequalities has been under rapid development, based on complex analysis
and strongly influenced by 'real-life' application. Many, but of course
not all, moving free (Le., a priori un- known) boundary problems
originating from engineering and economic applica- tions can directly,
or after a transformation, be formulated as variational inequal- ities.
In this work we investigate an evolutionary variational inequality with
a memory term which is, as a fixed domain formulation, the result of the
application of such a transformation to a degenerate moving free
boundary problem. This study includes mathematical modelling, existence,
uniqueness and regularity results, numerical analysis of finite element
and finite volume approximations, as well as numerical simulation
results for applications in polymer processing. Essential parts of these
research notes were developed during my work at the Chair of Applied
Mathematics (LAM) of the Technical University Munich. I would like to
express my sincerest gratitude to K. -H. Hoffmann, the head of this
chair and the present scientific director of the Center of Advanced
European Studies and Research (caesar), for his encouragement and
support. With this work I am fol- lowing a general concept of Applied
Mathematics to which he directed my interest and which, based on
application problems, comprises mathematical modelling, mathematical and
numerical analysis, computational aspects and visualization of
simulation results.