A nonlinear mathematical model for two-phase flow in nanoporous media
| dc.contributor.author | Melzi, Imane | |
| dc.contributor.author | Atik, Youcef | |
| dc.date.accessioned | 2023-04-12T16:12:30Z | |
| dc.date.available | 2023-04-12T16:12:30Z | |
| dc.date.issued | 2022-02-28 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 33 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Melzi, 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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16562 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Nonlinear system | |
| dc.subject | Nanoporous media | |
| dc.subject | Rothe's method | |
| dc.subject | Galerkin's method | |
| dc.title | A nonlinear mathematical model for two-phase flow in nanoporous media | en_US |
| dc.type | Article |