A multiscale colloid transport model with anisotropic degenerate diffusion

We 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‐posedness of the system using a L¹ 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.