Cross-diffusion systems coupled via a moving interface
<|reference_start|>Cross-diffusion systems coupled via a moving interface: We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin films. In our model, cross-diffusion of the various chemical species can be respectively modelled by a size-exclusion system for the solid phase and the Stefan-Maxwell system for the gaseous phase. The coupling between the two phases is modelled by linear phase transition laws of Butler-Volmer type, resulting in an interface evolution. The continuous properties of the model are investigated, in particular its entropy variational structure and stationary states. We introduce a two-point flux approximation finite volume scheme. The moving interface is addressed with a moving-mesh approach, where the mesh is locally deformed around the interface. The resulting discrete nonlinear system is shown to admit a solution that preserves the main properties of the continuous system, namely: mass conservation, nonnegativity, volume-filling constraints, decay of the free energy and asymptotics. In particular, the moving-mesh approach is compatible with the entropy structure of the continuous model. Numerical results illustrate these properties and the dynamics of the model.<|reference_end|>
@article{cancès2024cross-diffusion,
    title={Cross-diffusion systems coupled via a moving interface},
    author={Cl'ement Canc`es (RAPSODI, LPP), Jean Cauvin-Vila (TU Wien, TU
  Wien), Claire Chainais-Hillairet (LPP, RAPSODI ), Virginie Ehrlacher (ENPC,
  MATHERIALS)},
    journal={arXiv preprint arXiv:2407.15457},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.15457},
    primaryClass={math.AP cs.NA math.NA}
}