Local Behavior Analysis of Wetting Fronts for Pseudo‐Parabolic Diffusion–Convection Equation

In this paper, we consider a gravity‐driven unsaturated two‐phase flow with nonequilibrium formalism proposed by Hassanizadeh and coworkers. The nonequilibrium effect stems from the dynamic capillary pressure in porous media flow. Consequently, the resulting model is a nonlinear, degenerate pseudo‐parabolic diffusion–convection equation. We delve into illustrating and analyzing how the dynamic capillary effect and gravity introduce qualitative differences in the local behavior of wetting saturation fronts in the vicinity of the interface. The underlying idea is to analyze the traveling wave solutions and subsequently perform an asymptotic analysis on solutions with initial support in a half line.