Wall driven steady flow and heat transfer in a porous tube
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O. D. Makinde, Y. A. S. Aregbesola, S. A. Odejide (2006)
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We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.