Final Report on the DFG project "On the analysis of a class of cross-diffusion Cahn-Hilliard systems"

Abstract

In this project we considered a class of cross-diffusion systems involving Cahn-Hilliard terms and gave exhaustive answers to some main questions related to it. This class arises when modeling mixtures composed of several species that interact with one another with cross-diffusion effects and also have the tendency to separate from each other. In the case under consideration, there is only one species (that accounts for the void) which does separate from all the others. The interest for such a model stems from the fact that in many real world applications there exist multiphase systems where miscible entities do coexist in one single phase of the system. Our project started from an existing model and, by making a combination of both numerical and theoretical approaches, provided a systematical analysis to some core topics related to it, in order to gain a better understanding of the dynamics of the model and of its stationary solutions.