Multiscale Hyperbolic-Parabolic Models for Nonlinear Reactive Transport in Heterogeneously Fractured Porous Media

We study nonlinear reactive transport in a layered porous medium separated by an $\epsilon$-thin, highly heterogeneous fracture whose aperture and obstacle pattern vary periodically. Species transport in the bulk is governed by parabolic reaction–diffusion equations, coupled to a convection-diffusion-reaction problem in the fracture with nonlinear wall and obstacle reactions and Peclet number of order $O({\epsilon }^{-1})$. Via multiscale analysis as $\epsilon \to 0$, when the fracture collapses to a flat interface, we derive a new type of homogenized model consisting of bulk diffusion–reaction equations coupled through nonlinear interface conditions and a first-order semilinear hyperbolic system on the interface. We prove well-posedness and regularity of the limit system, construct a multiscale approximation with boundary-layer correctors, and derive quantitative error estimates in suitable energy norms.