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The confined Muskat problem: differences with the deep water regime. (English) Zbl 1301.35102

Summary: We study the evolution of the interface given by two incompressible fluids with different densities in the porous strip. This problem is known as the Muskat problem and is analogous to the two phase Hele-Shaw cell. The main goal of this paper is to compare the qualitative properties between the model when the fluids move without boundaries and the model when the fluids are confined. We find that, in a precise sense, the boundaries decrease the diffusion rate and the system becomes more singular.

MSC:

35Q35 PDEs in connection with fluid mechanics
35R35 Free boundary problems for PDEs
76D27 Other free boundary flows; Hele-Shaw flows
76S05 Flows in porous media; filtration; seepage
76T99 Multiphase and multicomponent flows
35B50 Maximum principles in context of PDEs
35B44 Blow-up in context of PDEs
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