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

• Applicant: Greta Marino, Ph.D.
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 496629752

The aim of this project is to provide a detailed study on a class of cross-diffusion systems involving Cahn-Hilliard terms. This class arises in modeling mixtures composed of several species that interact with one another via cross-diffusion effects and also have the tendency to separate. 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. Our project will start from an existing model and aims to give exhaustive answers to several open questions related to its analysis. We will make use of both numerical and theoretical approaches that will give a better understanding of the dynamics of the model and its stationary solutions, as well as randomness in the data.

• DFG Programme: Research Grants