Influence of a nonlinear degenerate diffusion on an advection-diffusion equation in a diffuse interface framework

This work is motivated by the modelling a liquid-vapour flows with phase transition describing evolution of coolant within an heat exchanger (e.g. core Pressurized Water Reactor). We investigate advection-diffusion equation degenerate and nonlinear diffusion coefficient. The degeneracy corresponds to liquid-vapor mixture in original model whereas coefficient non-degenerate pure cases. focus on influence simple 1D configuration for which some analytical computations can be done, leading surprising behavior respect diffusion.