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

[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.

[学科分类] 数学（综合）

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