Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Chemetov N.V.   Neves W.  

Solvability of a generalized Buckley-Leverett System

Reporter: Chemetov N.V.

We propose a new mathematical modeling of the Buckley- Leverett system, which describes the two-phase flows in porous media. We prove the solvability of the initial-boundary value problem for a deduced model. In order to show the solvability result, we consider an approximated parabolic-elliptic system. Since the approximated solutions do not have any type compactness property, the limit transition is justified by the kinetic method [1]-[3]. The main issue is to study a linear (kinetic) transport equation, instead of the nonlinear original system

1. Chemetov N.V., Neves W. The generalized Buckley-Leverett System. Solvability // submitted to Arch. Rational Mech. Anal.,
2. Chemetov N.V., Arruda L. L p-Solvability of a Full Superconductive Model // Non-linear Analysis: Real World Applications, published online, 2011.
3. Chemetov N.V. Nonlinear Hyperbolic-Elliptic Systems in the Bounded Domain // To appear in: Communications on Pure and Applied Analysis.

Abstracts file: 2.pdf
Full text file: Chemetov&Neves.pdf

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