GRK-Kolloquium, Dr. Greta Marino

On the analysis of a class of cross-diffusion systems with Cahn-Hilliard terms

Abstract: The aim of this talk is to introduce a class of
cross-diffusion systems involving Cahn-Hilliard terms. This class arises
in modelling 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, only one
species (that accounts for the void) does separate from 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 may
coexist in one single phase of the system.
After an introduction of the model, we will present some results on
existence of weak and stationary solutions, and then conclude with an
outlook to some future developments.
This talk is based on joint works with Jean Cauvin-Vila, Virginie
Ehrlacher and Jan-Frederik Pietschmann.