Imane Melzi, Youcef Atik
Abstract:
We propose a mathematical model for the two-phase flow nanoporous media.
Unlike classical models, our model suppose that the rock permeability depends on
the gradient of pressure. Using usual laws of flows in porous media, we obtain a system
of two nonlinear partial differential equations: the first is elliptic and the second
is parabolic degenerate. We study a regularized version of our model, obtained
by adding a ``vanishing'' term to the coefficient causing the degeneracy.
We prove the existence of a weak solution of the regularized model. Our approach
consists essentially to use the Rothe's method coupled with Galerkin's method.
Submitted January 31, 2021. Published February 28, 2022.
Math Subject Classifications: 35M32, 76T99, 74F10.
Key Words: Nonlinear system; nanoporous media; Rothe's method; Galerkin's method.
DOI: https://doi.org/10.58997/ejde.2022.15
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Imane Melzi Laboratory of nonlinear partial differential equations and history of mathematics department of mathematics Ecole Normale Supérieure Kouba, Algiers, Algeria email: imane.melzi@g.ens-kouba.dz |
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Youcef Atik Laboratory of nonlinear partial differential equations and history of mathematics department of mathematics Ecole Normale Supérieure Kouba, Algiers, Algeria email: youcefatiq@gmail.com |
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