A nonlinear mathematical model for two-phase flow in nanoporous media

Electronic Journal of Differential Equations

article

Imane Melzi¹  Youcef Atik¹ 

[1] Laboratory of nonlinear partial differential equations and history of mathematics department of mathematics Ecole Normale Supérieure Kouba

关键词: Nonlinear system;    nanoporous media;    Rothe's method;    Galerkin's method.;   

DOI  :  10.58997/ejde.2022.15

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

We propose a mathematical model for the two-phase flow nanoporous media. Unlike classical models, our model suppose that the rock permeability depends onthe gradient of pressure. Using usual laws of flows in porous media, we obtain a systemof two nonlinear partial differential equations: the first is elliptic and the secondis 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 approachconsists essentially to use the Rothe's method coupled with Galerkin's method.

【 授权许可】

CC BY