06.12.2018 15:45 Clément Cancès (Université Lille 1 & CNRS):
Long time behaviour of a reduced model for two-phase flows in porous mediaMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

We consider a thin film approximation for two-phase porous media that is derived thanks to Dupuit’s approximation. The model then boils down to a degenerate cross diffusion system that can be seen as a generalisation of the porous medium equation. This system can be interpreted as the Wasserstein gradient flow of some energy. The solutions converge as time goes to infinity towards some self similar solutions, that can correspond to minimizers of some modified energy after proper rescaling. The shape of these minimizers strongly depends on the parameter range. Finally, we study numerically the convergence rate as time goes to infinity thanks to an energy diminishing finite volume scheme. (joint work with A. Ait Hammou Oulhaj, C. Chainais-Hillairet and P. Laurençot)