Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 15, pp. 1-33.

Title: A nonlinear mathematical model for two-phase flow in nanoporous media
       
Authors: Imane Melzi (Ecole Normale Superieure, Kouba, Algiers, Algeria)
         Youcef Atik (Ecole Normale Superieure, Kouba, Algiers, Algeria)

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.