The reducibility of the anisotropic Hele-Shaw problem to the isotropic case |
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| Institution: | 1. Dipartimento di Matematica F. Enriques, Università degli Studi di Milano, Milano I-20133, Italy;2. Dipartimento di Matematica, Politecnico di Milano, Milano I-20133, Italy;3. Czech Academy of Sciences, CZ-11567 Praha 1, Czech Republic;1. ExxonMobil Upstream Research Company, P.O. Box 2189, Houston, TX 77252, USA;2. Department of Civil & Environmental Engineering, Duke University, Room 121 Hudson Hall, P.O. Box 90287, Durham, NC 27708-0287, USA;1. Department of Mathematics, Jinan University, Guangzhou, 510632, PR China;2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, 221116, PR China;3. School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, PR China |
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| Abstract: | 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. |
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