On the Diffusion of Immiscible Fluids in Porous Media
C. J. van Duyn · SIAM Journal on Mathematical Analysis · 1979
From the mathematical formulation of the diffusion of two immiscible fluids, we arrive at a nonlinear two-sided degenerate parabolic equation. Existence, uniqueness and a weak maximum principle are proved for the Cauchy problem in the half plane $x \in \mathbb{R}$, $t > 0$. Furthermore, it is shown that the solutions of a class of Cauchy problems converge towards a similarity solution as $t \to \infty $ and the rate of convergence is discussed.