Convection in porous media plays a central role in geophysical fluid dynamics, geothermal energy, carbon sequestration, and other climate-related processes. Layered porous structures often arise naturally or through design, leading to systems with abrupt material transitions. In such cases, the Darcy–Boussinesq equations give rise to a nonlinear transmission problem, raising a fundamental question: what interfacial conditions are appropriate? In this talk, I address this issue by viewing the sharp interface model as the limit of a more physically realistic diffuse-interface formulation, where properties vary smoothly across layers. Assuming constant porosity, we prove that as the transition-layer thickness vanishes, solutions of the diffuse model converge to those of the sharp interface system over finite time intervals for suitable data. The analysis highlights velocity boundary layer formation and requires delicate elliptic and parabolic estimates with nearly discontinuous coefficients. Beyond finite time, we show that both sharp and diffuse models admit global attractors, and these attractors converge as the transition layers shrink. This work provides a rigorous foundation for the sharp interface approximation, linking it to more realistic diffuse-interface models. I will also discuss implications for long-time dynamics and outline numerical methods adapted to layered porous structures. This is joint work with Hongjie Dong (Brown University) and Kaijian Sha (EIT). | 