A multiscale colloid transport model with anistropic degenerate diffusion

International audienceWe consider a weakly coupled semilinear parabolic-hyperbolic system with a degenerate and anisotropic diffusion. It arises to model the evolution of a chemical or biological tracer in a porous medium. We study the well-posed- ness of the system using a L^1 theory. Then, we establish the relaxation limit as the reaction constant becomes large. We prove that the system converges to a nonlinear parabolic-hyperbolic equation that generalizes the Stefan problem. Two specificities of this paper are (i) to deal with ill-prepared initial data and (ii) with unique entropy solutions based on a precise entropy inequality