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., http://arxiv.org/abs/1011.5461.
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.
| Файл тезисов: | 2.pdf |
| Файл с полным текстом: | Chemetov&Neves.pdf |