M 643

It is well known that material scientists consider evolution equations associated to energy functionals that are not convex. As this results in a forward-backward parabolic problem, a higher order term is usually added to deal with the inherent instability. In this talk we present a one dimensional model that fits this framework. After discussing some ideas for the analysis of the stationary case, we consider the evolution of the regularized problem from a numerical point of view. We provide a suitable finite element scheme and show some simulations that illustrate the behavior of the flow.

Prof. Dr. Paola Pozzi

Universität Duisburg-Essen