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Non-equilibrium imbibition of a porous block

Published online by Cambridge University Press:  26 September 2008

Arkady Gilman
Arkady Gilman
Affiliation:
Faculty of Civil Engineering, Technion – Israel Institute of Technology, Haifa, Israel
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Abstract

We consider a phenomenological model proposed by Barenblatt [1] for non-equilibrium two-phase flow in porous media. In the case of zero total flow it reduces to a pair of equations:

where Φ(σ) is a non-decreasing (not necessarily increasing) smooth function defined in the interval 0 ≤ σ ≤ 1. We consider initial-boundary problems for this system in which the initial data are given only for s, and the boundary data only for ς (which corresponds to the physical sense of the model). The degenerate character of the system allows us to apply simple topological methods. We show that the boundary problem is well-posed, in the sense that there exits a unique (weak) solution which satisfies the maximum principle and depends continuously on the initial data. The solution is no less smooth than the initial and boundary data.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 1 , February 1996 , pp. 43 - 52
Copyright
Copyright © Cambridge University Press 1996

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References

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