Melzi, ImaneAtik, Youcef2023-04-122023-04-122022-02-28Melzi, I., & Atik, Y. (2022). A nonlinear mathematical model for two-phase flow in nanoporous media. <i>Electronic Journal of Differential Equations, 2022</i>(15), pp. 1-33.1072-6691https://hdl.handle.net/10877/16562We 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.Text33 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear systemNanoporous mediaRothe's methodGalerkin's methodArticle