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

It is established that the unilateral Hele-Shaw problem for flows in a channel when there is bulk anisotropy and Saffman–Taylor boundary conditions on the free boundary can be reduced to the isotropic case using a linear non-orthogonal coordinate transformation. Correspondingly, any exact solution of the Hele-Shaw problem for an isotropic medium generates a set of solutions for an anisotropic medium for arbitrary orientation of the principal axes of the permeability tensor with respect to the direction of the channel axis.