The reducibility of the anisotropic Hele-Shaw problem to the isotropic case

An asymptotic analysis of the steady process of saturation of a laminated porous material

“…The error in determining the radius of curvature of the interface at the point D is of the same order. Hence, asymptotic expansion (4.1), (4.2) of the solution of problem (2.10) satisfactorily describes the configuration of the interface DC for = 0.1 down to a small neighbourhood of the point D. Note also that, using a non-orthogonal expansion of the coordinates, similar to that described earlier, 9 the results obtained can be extended to the case of extremely anisotropic layers.…”

Evolution of the interface in a stratified anisotropic porous material

“…It should be noted that the last condition is not identical to condition (1.5) (this condition is discussed in [3,6] for the Hele-Shaw problem, and in [7] for the related Stefan problem).…”