In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the present paper, we give a new definition of generalized practical stability (abbreviated as GP-stability) and...
Models of two phase flows in porous media, used in petroleum engineering, lead to a system of two coupled equations with elliptic and parabolic degenerate terms, and two unknowns, the saturation and the pressure. For the purpose of their approximation, a coupled scheme, consisting in a finite volume method together with a phase-by-phase upstream weighting scheme, is used in the industrial setting. This paper presents a mathematical analysis of this coupled scheme, first showing that it satisfies...
Models of two phase flows in porous media, used in petroleum
engineering, lead to a system of two coupled equations with elliptic
and parabolic degenerate terms, and two unknowns,
the saturation and the pressure.
For the purpose of their approximation, a coupled scheme, consisting in
a finite volume method together with
a phase-by-phase upstream weighting scheme, is used in the industrial setting.
This paper presents a mathematical analysis of this coupled scheme, first showing
that it satisfies...
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