Anisotropic flows of Forchheimer-type in porous media and their steady states
We study the anisotropic Forchheimer-typed flows for compressible fluids in porous media. The first half of the paper is devoted to understanding the nonlinear structure of the anisotropic momentum equations. Unlike the isotropic flows, the important monotonicity properties are not automatically sat...
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| Published in | Nonlinear analysis: real world applications Vol. 84; p. 104269 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.08.2025
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| ISSN | 1468-1218 |
| DOI | 10.1016/j.nonrwa.2024.104269 |
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| Abstract | We study the anisotropic Forchheimer-typed flows for compressible fluids in porous media. The first half of the paper is devoted to understanding the nonlinear structure of the anisotropic momentum equations. Unlike the isotropic flows, the important monotonicity properties are not automatically satisfied in this case. Therefore, various sufficient conditions for them are derived and applied to the experimental data. In the second half of the paper, we prove the existence and uniqueness of the steady state flows subject to a nonhomogeneous Dirichlet boundary condition. It is also established that these steady states, in appropriate functional spaces, have local Hölder continuous dependence on the forcing function and the boundary data. |
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| AbstractList | We study the anisotropic Forchheimer-typed flows for compressible fluids in porous media. The first half of the paper is devoted to understanding the nonlinear structure of the anisotropic momentum equations. Unlike the isotropic flows, the important monotonicity properties are not automatically satisfied in this case. Therefore, various sufficient conditions for them are derived and applied to the experimental data. In the second half of the paper, we prove the existence and uniqueness of the steady state flows subject to a nonhomogeneous Dirichlet boundary condition. It is also established that these steady states, in appropriate functional spaces, have local Hölder continuous dependence on the forcing function and the boundary data. |
| ArticleNumber | 104269 |
| Author | Hoang, Luan Kieu, Thinh |
| Author_xml | – sequence: 1 givenname: Luan orcidid: 0000-0002-8008-4915 surname: Hoang fullname: Hoang, Luan email: luan.hoang@ttu.edu organization: Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409–1042, USA – sequence: 2 givenname: Thinh surname: Kieu fullname: Kieu, Thinh email: thinh.kieu@ung.edu organization: Department of Mathematics, University of North Georgia, Gainesville Campus, 3820 Mundy Mill Rd., Oakwood, GA 30566, USA |
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| Cites_doi | 10.1023/A:1011543412675 10.1007/s10958-015-2576-1 10.1016/j.jde.2016.10.043 10.1016/0362-546X(89)90093-X 10.1007/PL00001527 10.1007/s11854-018-0064-5 10.1023/A:1010749114251 10.1007/BF00141261 10.1088/0951-7715/29/3/1124 10.1007/BF01385609 10.1137/S0036141095290562 10.1007/BF00192152 10.1051/m2an/1993270201311 10.1016/0309-1708(81)90025-7 10.1098/rspa.2003.1169 10.1063/1.4976195 10.55730/1300-0098.3405 10.1111/1467-9590.00142 10.1063/1.3204977 10.1007/BF01396320 10.1007/BF01036526 10.1111/1467-9590.00116 10.1029/TR039i004p00702 10.1007/s10958-014-2045-2 10.1088/1361-6544/aabf05 |
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| Keywords | Porous media Nonlinear partial differential equations Forchheimer Anisotropic First-order system Fluid flows Monotonicity |
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| References | Celik, Hoang, Kieu (b36) 2023; 47 Forchheimer (b2) 1901; 45 Celik, Hoang (b35) 2017; 262 Scheidegger (b7) 1974 Celik, Hoang (b37) 2016; 29 Hoang, Ibragimov (b30) 2012; 17 Baranger, Najib (b40) 1990; 58 Irmay (b8) 1965; 29 Hoang, Kieu (b31) 2019; 137 Celik, Hoang, Kieu (b34) 2018; 31 Ergun (b6) 1952; 48 Irmay (b11) 1958; 39 Franchi, Straughan (b22) 2003; 459 Chow (b39) 1989; 54 Bear (b10) 1988 Hassanizadeh, Gray (b19) 1987; 2 Vázquez (b20) 2007 Chadam, Qin (b27) 1997; 28 Glowinski, Marroco (b38) 1975; 9 Payne, Straughan (b24) 1999; 102 Zeidler (b44) 1990 Muskat (b5) 1937 Forchheimer (b3) 1930 Chen, Lyons, Qin (b12) 2001; 44 Ewing, Lazarov, Lyons, Papavassiliou, Pasciak, Qin (b13) 1999; 3 Bachmat (b16) 1965; 1 Payne, Straughan (b25) 2000; 105 Cvetković (b18) 1986; 1 Fabrie (b21) 1989; 13 Ahmed (b9) 1967 Payne, Song (b26) 2000; 51 Hoang, Ibragimov, Kieu, Sobol (b33) 2015; 210 Ward (b4) 1964; 90(HY5) Barak, Bear (b17) 1981; 4 Payne, Straughan (b23) 1996; 75 Celik, Hoang, Ibragimov, Kieu (b43) 2017; 58 Nield, Bejan (b15) 2013 Straughan (b28) 2008; vol. 165 Hoang, Kieu, Phan (b32) 2014; 202 Whitaker (b14) 1996; 25 Sandri (b41) 1993; 27 Aulisa, Bloshanskaya, Hoang, Ibragimov (b29) 2009; 50 Dupuit (b1) 1857; 45 Knabner, Summ (b42) 2016 Chen (10.1016/j.nonrwa.2024.104269_b12) 2001; 44 Cvetković (10.1016/j.nonrwa.2024.104269_b18) 1986; 1 Bear (10.1016/j.nonrwa.2024.104269_b10) 1988 Scheidegger (10.1016/j.nonrwa.2024.104269_b7) 1974 Payne (10.1016/j.nonrwa.2024.104269_b23) 1996; 75 Glowinski (10.1016/j.nonrwa.2024.104269_b38) 1975; 9 Nield (10.1016/j.nonrwa.2024.104269_b15) 2013 Ergun (10.1016/j.nonrwa.2024.104269_b6) 1952; 48 Hoang (10.1016/j.nonrwa.2024.104269_b30) 2012; 17 Sandri (10.1016/j.nonrwa.2024.104269_b41) 1993; 27 Hassanizadeh (10.1016/j.nonrwa.2024.104269_b19) 1987; 2 Payne (10.1016/j.nonrwa.2024.104269_b25) 2000; 105 Hoang (10.1016/j.nonrwa.2024.104269_b31) 2019; 137 Irmay (10.1016/j.nonrwa.2024.104269_b8) 1965; 29 Celik (10.1016/j.nonrwa.2024.104269_b43) 2017; 58 Barak (10.1016/j.nonrwa.2024.104269_b17) 1981; 4 Aulisa (10.1016/j.nonrwa.2024.104269_b29) 2009; 50 Franchi (10.1016/j.nonrwa.2024.104269_b22) 2003; 459 Chow (10.1016/j.nonrwa.2024.104269_b39) 1989; 54 Ewing (10.1016/j.nonrwa.2024.104269_b13) 1999; 3 Ahmed (10.1016/j.nonrwa.2024.104269_b9) 1967 Chadam (10.1016/j.nonrwa.2024.104269_b27) 1997; 28 Forchheimer (10.1016/j.nonrwa.2024.104269_b2) 1901; 45 Irmay (10.1016/j.nonrwa.2024.104269_b11) 1958; 39 Vázquez (10.1016/j.nonrwa.2024.104269_b20) 2007 Bachmat (10.1016/j.nonrwa.2024.104269_b16) 1965; 1 Fabrie (10.1016/j.nonrwa.2024.104269_b21) 1989; 13 Hoang (10.1016/j.nonrwa.2024.104269_b32) 2014; 202 Ward (10.1016/j.nonrwa.2024.104269_b4) 1964; 90(HY5) Baranger (10.1016/j.nonrwa.2024.104269_b40) 1990; 58 Payne (10.1016/j.nonrwa.2024.104269_b24) 1999; 102 Hoang (10.1016/j.nonrwa.2024.104269_b33) 2015; 210 Forchheimer (10.1016/j.nonrwa.2024.104269_b3) 1930 Celik (10.1016/j.nonrwa.2024.104269_b35) 2017; 262 Dupuit (10.1016/j.nonrwa.2024.104269_b1) 1857; 45 Knabner (10.1016/j.nonrwa.2024.104269_b42) 2016 Straughan (10.1016/j.nonrwa.2024.104269_b28) 2008; vol. 165 Celik (10.1016/j.nonrwa.2024.104269_b36) 2023; 47 Zeidler (10.1016/j.nonrwa.2024.104269_b44) 1990 Payne (10.1016/j.nonrwa.2024.104269_b26) 2000; 51 Muskat (10.1016/j.nonrwa.2024.104269_b5) 1937 Whitaker (10.1016/j.nonrwa.2024.104269_b14) 1996; 25 Celik (10.1016/j.nonrwa.2024.104269_b34) 2018; 31 Celik (10.1016/j.nonrwa.2024.104269_b37) 2016; 29 |
| References_xml | – volume: 90(HY5) start-page: 1 year: 1964 end-page: 12 ident: b4 article-title: Turbulent flow in porous media publication-title: J. Hydraulics Div. Proc. Am. Soc. Civ. Eng. – volume: 9 start-page: 41 year: 1975 end-page: 76 ident: b38 article-title: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires publication-title: Rev. française d’automat. informat. rech. opérationnelle. Anal. numér. – volume: 44 start-page: 325 year: 2001 end-page: 335 ident: b12 article-title: Derivation of the Forchheimer law via homogenization publication-title: Transp. Porous Media – start-page: xxii+624 year: 2007 ident: b20 article-title: The porous medium equation publication-title: Oxford Mathematical Monographs – volume: 31 start-page: 3617 year: 2018 end-page: 3650 ident: b34 article-title: Doubly nonlinear parabolic equations for a general class of Forchheimer gas flows in porous media publication-title: Nonlinearity – year: 1990 ident: b44 article-title: Nonlinear functional analysis and its applications. II/b – volume: 1 start-page: 63 year: 1965 end-page: 75 ident: b16 article-title: Basic transport coefficients as aquifer characteristics publication-title: I.A.S.H. Proceedings of the Dubrovnik symposium on hydrology of fractured rocks – volume: 1 start-page: 63 year: 1986 end-page: 97 ident: b18 article-title: A continuum approach to high velocity flow in a porous medium publication-title: Transp. Porous Media – volume: 27 start-page: 131 year: 1993 end-page: 155 ident: b41 article-title: Sur lápproximation numérique des écoulements quasi-newtoniens dont la viscosité suit la loi puissance ou la loi de carreau publication-title: ESAIM: M2AN – volume: 17 start-page: 511 year: 2012 end-page: 556 ident: b30 article-title: Qualitative study of generalized Forchheimer flows with the flux boundary condition publication-title: Adv. Differential Equations – volume: 202 start-page: 259 year: 2014 end-page: 332 ident: b32 article-title: Properties of generalized Forchheimer flows in porous media publication-title: J. Math. Sci. – year: 1967 ident: b9 article-title: Physical properties of porous medium affecting laminar and turbulent flow of water – volume: 13 start-page: 1025 year: 1989 end-page: 1049 ident: b21 article-title: Regularity of the solution of Darcy-Forchheimer’s equation publication-title: Nonlinear Anal. – volume: 210 start-page: 476 year: 2015 end-page: 544 ident: b33 article-title: Stability of solutions to generalized Forchheimer equations of any degree publication-title: J. Math. Sci. (N. Y.) – volume: 2 start-page: 521 year: 1987 end-page: 531 ident: b19 article-title: High velocity flow in porous media publication-title: Transp. Porous Media – volume: 45 start-page: 92 year: 1857 end-page: 96 ident: b1 article-title: Mouvement de l’eau a travers le terrains permeables publication-title: C. R. Hebd. Seances Acad. Sci. – volume: 102 start-page: 419 year: 1999 end-page: 439 ident: b24 article-title: Convergence and continuous dependence for the Brinkman-Forchheimer equations publication-title: Stud. Appl. Math. – volume: 51 start-page: 867 year: 2000 end-page: 889 ident: b26 article-title: Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows publication-title: Z. Angew. Math. Phys. – volume: 262 start-page: 2158 year: 2017 end-page: 2195 ident: b35 article-title: Maximum estimates for generalized Forchheimer flows in heterogeneous porous media publication-title: J. Differential Equations – volume: 48 start-page: 89 year: 1952 end-page: 94 ident: b6 article-title: Fluid flow through packed columns publication-title: Chem. Eng. Prog. – volume: 58 start-page: 35 year: 1990 end-page: 49 ident: b40 article-title: Numerical analysis of quasi-Newtonian flow obeying the power low or the carreau flow publication-title: Numer. Math. – volume: 39 start-page: 702 year: 1958 end-page: 707 ident: b11 article-title: On the theoretical derivation of Darcy and Forchheimer formulas publication-title: EOS Trans. Am. Geophys. Union – volume: 25 start-page: 27 year: 1996 end-page: 61 ident: b14 article-title: The Forchheimer equation: A theoretical development publication-title: Transp. Porous Media – start-page: 1 year: 2016 end-page: 26 ident: b42 article-title: Solvability of the mixed formulation for Darcy-Forchheimer flow in porous media – year: 1988 ident: b10 article-title: Dynamics of Fluids in Porous Media – volume: 137 start-page: 1 year: 2019 end-page: 55 ident: b31 article-title: Global estimates for generalized Forchheimer flows of slightly compressible fluids publication-title: J. Anal. Math. – volume: 54 start-page: 373 year: 1989 end-page: 393 ident: b39 article-title: Finite element error estimates for non-linear elliptic equations of monotone type publication-title: Numer. Math. – volume: 45 start-page: 1781 year: 1901 end-page: 1788 ident: b2 article-title: Wasserbewegung durch boden publication-title: Zeit. Ver. Deut. Ing. – year: 1937 ident: b5 article-title: The flow of homogeneous fluids through porous media – volume: 28 start-page: 808 year: 1997 end-page: 830 ident: b27 article-title: Spatial decay estimates for flow in a porous medium publication-title: SIAM J. Math. Anal. – volume: 75 start-page: 225 year: 1996 end-page: 271 ident: b23 article-title: Stability in the initial-time geometry problem for the Brinkman and Darcy equations of flow in porous media publication-title: J. Math. Pures Appl. (9) – year: 2013 ident: b15 article-title: Convection in porous media – volume: 4 start-page: 54 year: 1981 end-page: 66 ident: b17 article-title: Flow at high Reynolds numbers through anisotropic porous media publication-title: Adv. Water Resour. – volume: 29 start-page: 1124 year: 2016 end-page: 1155 ident: b37 article-title: Generalized Forchheimer flows in heterogeneous porous media publication-title: Nonlinearity – year: 1974 ident: b7 article-title: The physics of flow through porous media – volume: 105 start-page: 59 year: 2000 end-page: 81 ident: b25 article-title: Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium publication-title: Stud. Appl. Math. – volume: 58 year: 2017 ident: b43 article-title: Fluid flows of mixed regimes in porous media publication-title: J. Math. Phys. – volume: 3 start-page: 185 year: 1999 end-page: 204 ident: b13 article-title: Numerical well model for non-Darcy flow through isotropic porous media publication-title: Comput. Geosci. – year: 1930 ident: b3 article-title: Hydraulik – volume: vol. 165 start-page: xiv+437 year: 2008 ident: b28 publication-title: Stability and wave motion in porous media – volume: 50 year: 2009 ident: b29 article-title: Analysis of generalized Forchheimer flows of compressible fluids in porous media publication-title: J. Math. Phys. – volume: 47 start-page: 949 year: 2023 end-page: 987 ident: b36 article-title: Studying a doubly nonlinear model of slightly compressible Forchheimer flows in rotating porous media publication-title: Turkish J. Math. – volume: 29 start-page: 37 year: 1965 end-page: 43 ident: b8 article-title: Theoretical models of flow through porous media publication-title: Bull. R.I.L.E.M – volume: 459 start-page: 3195 year: 2003 end-page: 3202 ident: b22 article-title: Continuous dependence and decay for the Forchheimer equations publication-title: R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. – volume: 90(HY5) start-page: 1 year: 1964 ident: 10.1016/j.nonrwa.2024.104269_b4 article-title: Turbulent flow in porous media publication-title: J. Hydraulics Div. Proc. Am. Soc. Civ. Eng. – volume: 3 start-page: 185 issue: 3–4 year: 1999 ident: 10.1016/j.nonrwa.2024.104269_b13 article-title: Numerical well model for non-Darcy flow through isotropic porous media publication-title: Comput. Geosci. doi: 10.1023/A:1011543412675 – volume: 210 start-page: 476 year: 2015 ident: 10.1016/j.nonrwa.2024.104269_b33 article-title: Stability of solutions to generalized Forchheimer equations of any degree publication-title: J. Math. Sci. (N. Y.) doi: 10.1007/s10958-015-2576-1 – volume: 262 start-page: 2158 issue: 3 year: 2017 ident: 10.1016/j.nonrwa.2024.104269_b35 article-title: Maximum estimates for generalized Forchheimer flows in heterogeneous porous media publication-title: J. Differential Equations doi: 10.1016/j.jde.2016.10.043 – volume: 13 start-page: 1025 issue: 9 year: 1989 ident: 10.1016/j.nonrwa.2024.104269_b21 article-title: Regularity of the solution of Darcy-Forchheimer’s equation publication-title: Nonlinear Anal. doi: 10.1016/0362-546X(89)90093-X – volume: 17 start-page: 511 issue: 5–6 year: 2012 ident: 10.1016/j.nonrwa.2024.104269_b30 article-title: Qualitative study of generalized Forchheimer flows with the flux boundary condition publication-title: Adv. Differential Equations – volume: 29 start-page: 37 year: 1965 ident: 10.1016/j.nonrwa.2024.104269_b8 article-title: Theoretical models of flow through porous media publication-title: Bull. R.I.L.E.M – year: 1930 ident: 10.1016/j.nonrwa.2024.104269_b3 – volume: 51 start-page: 867 issue: 6 year: 2000 ident: 10.1016/j.nonrwa.2024.104269_b26 article-title: Spatial decay for a model of double diffusive convection in Darcy and Brinkman flows publication-title: Z. Angew. Math. Phys. doi: 10.1007/PL00001527 – volume: 137 start-page: 1 issue: 1 year: 2019 ident: 10.1016/j.nonrwa.2024.104269_b31 article-title: Global estimates for generalized Forchheimer flows of slightly compressible fluids publication-title: J. Anal. Math. doi: 10.1007/s11854-018-0064-5 – volume: 44 start-page: 325 issue: 2 year: 2001 ident: 10.1016/j.nonrwa.2024.104269_b12 article-title: Derivation of the Forchheimer law via homogenization publication-title: Transp. Porous Media doi: 10.1023/A:1010749114251 – year: 1967 ident: 10.1016/j.nonrwa.2024.104269_b9 – volume: 25 start-page: 27 issue: 1 year: 1996 ident: 10.1016/j.nonrwa.2024.104269_b14 article-title: The Forchheimer equation: A theoretical development publication-title: Transp. Porous Media doi: 10.1007/BF00141261 – year: 2013 ident: 10.1016/j.nonrwa.2024.104269_b15 – volume: 29 start-page: 1124 issue: 3 year: 2016 ident: 10.1016/j.nonrwa.2024.104269_b37 article-title: Generalized Forchheimer flows in heterogeneous porous media publication-title: Nonlinearity doi: 10.1088/0951-7715/29/3/1124 – volume: 58 start-page: 35 issue: 1 year: 1990 ident: 10.1016/j.nonrwa.2024.104269_b40 article-title: Numerical analysis of quasi-Newtonian flow obeying the power low or the carreau flow publication-title: Numer. Math. doi: 10.1007/BF01385609 – volume: 48 start-page: 89 year: 1952 ident: 10.1016/j.nonrwa.2024.104269_b6 article-title: Fluid flow through packed columns publication-title: Chem. Eng. Prog. – year: 1974 ident: 10.1016/j.nonrwa.2024.104269_b7 – start-page: 1 year: 2016 ident: 10.1016/j.nonrwa.2024.104269_b42 – volume: 28 start-page: 808 issue: 4 year: 1997 ident: 10.1016/j.nonrwa.2024.104269_b27 article-title: Spatial decay estimates for flow in a porous medium publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141095290562 – volume: 2 start-page: 521 issue: 6 year: 1987 ident: 10.1016/j.nonrwa.2024.104269_b19 article-title: High velocity flow in porous media publication-title: Transp. Porous Media doi: 10.1007/BF00192152 – volume: 27 start-page: 131 issue: 2 year: 1993 ident: 10.1016/j.nonrwa.2024.104269_b41 article-title: Sur lápproximation numérique des écoulements quasi-newtoniens dont la viscosité suit la loi puissance ou la loi de carreau publication-title: ESAIM: M2AN doi: 10.1051/m2an/1993270201311 – volume: 45 start-page: 92 year: 1857 ident: 10.1016/j.nonrwa.2024.104269_b1 article-title: Mouvement de l’eau a travers le terrains permeables publication-title: C. R. Hebd. Seances Acad. Sci. – year: 1988 ident: 10.1016/j.nonrwa.2024.104269_b10 – volume: 4 start-page: 54 issue: 2 year: 1981 ident: 10.1016/j.nonrwa.2024.104269_b17 article-title: Flow at high Reynolds numbers through anisotropic porous media publication-title: Adv. Water Resour. doi: 10.1016/0309-1708(81)90025-7 – volume: 75 start-page: 225 issue: 3 year: 1996 ident: 10.1016/j.nonrwa.2024.104269_b23 article-title: Stability in the initial-time geometry problem for the Brinkman and Darcy equations of flow in porous media publication-title: J. Math. Pures Appl. (9) – volume: 459 start-page: 3195 issue: 2040 year: 2003 ident: 10.1016/j.nonrwa.2024.104269_b22 article-title: Continuous dependence and decay for the Forchheimer equations publication-title: R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. doi: 10.1098/rspa.2003.1169 – volume: 58 issue: 2 year: 2017 ident: 10.1016/j.nonrwa.2024.104269_b43 article-title: Fluid flows of mixed regimes in porous media publication-title: J. Math. Phys. doi: 10.1063/1.4976195 – volume: 47 start-page: 949 issue: 3 year: 2023 ident: 10.1016/j.nonrwa.2024.104269_b36 article-title: Studying a doubly nonlinear model of slightly compressible Forchheimer flows in rotating porous media publication-title: Turkish J. Math. doi: 10.55730/1300-0098.3405 – volume: 105 start-page: 59 issue: 1 year: 2000 ident: 10.1016/j.nonrwa.2024.104269_b25 article-title: Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium publication-title: Stud. Appl. Math. doi: 10.1111/1467-9590.00142 – volume: 45 start-page: 1781 year: 1901 ident: 10.1016/j.nonrwa.2024.104269_b2 article-title: Wasserbewegung durch boden publication-title: Zeit. Ver. Deut. Ing. – volume: 1 start-page: 63 year: 1965 ident: 10.1016/j.nonrwa.2024.104269_b16 article-title: Basic transport coefficients as aquifer characteristics – volume: 50 issue: 10 year: 2009 ident: 10.1016/j.nonrwa.2024.104269_b29 article-title: Analysis of generalized Forchheimer flows of compressible fluids in porous media publication-title: J. Math. Phys. doi: 10.1063/1.3204977 – volume: 54 start-page: 373 issue: 4 year: 1989 ident: 10.1016/j.nonrwa.2024.104269_b39 article-title: Finite element error estimates for non-linear elliptic equations of monotone type publication-title: Numer. Math. doi: 10.1007/BF01396320 – volume: 1 start-page: 63 issue: 1 year: 1986 ident: 10.1016/j.nonrwa.2024.104269_b18 article-title: A continuum approach to high velocity flow in a porous medium publication-title: Transp. Porous Media doi: 10.1007/BF01036526 – volume: vol. 165 start-page: xiv+437 year: 2008 ident: 10.1016/j.nonrwa.2024.104269_b28 – year: 1937 ident: 10.1016/j.nonrwa.2024.104269_b5 – volume: 9 start-page: 41 issue: R2 year: 1975 ident: 10.1016/j.nonrwa.2024.104269_b38 article-title: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires publication-title: Rev. française d’automat. informat. rech. opérationnelle. Anal. numér. – volume: 102 start-page: 419 issue: 4 year: 1999 ident: 10.1016/j.nonrwa.2024.104269_b24 article-title: Convergence and continuous dependence for the Brinkman-Forchheimer equations publication-title: Stud. Appl. Math. doi: 10.1111/1467-9590.00116 – volume: 39 start-page: 702 issue: 4 year: 1958 ident: 10.1016/j.nonrwa.2024.104269_b11 article-title: On the theoretical derivation of Darcy and Forchheimer formulas publication-title: EOS Trans. Am. Geophys. Union doi: 10.1029/TR039i004p00702 – start-page: xxii+624 year: 2007 ident: 10.1016/j.nonrwa.2024.104269_b20 article-title: The porous medium equation – volume: 202 start-page: 259 issue: 2 year: 2014 ident: 10.1016/j.nonrwa.2024.104269_b32 article-title: Properties of generalized Forchheimer flows in porous media publication-title: J. Math. Sci. doi: 10.1007/s10958-014-2045-2 – volume: 31 start-page: 3617 issue: 8 year: 2018 ident: 10.1016/j.nonrwa.2024.104269_b34 article-title: Doubly nonlinear parabolic equations for a general class of Forchheimer gas flows in porous media publication-title: Nonlinearity doi: 10.1088/1361-6544/aabf05 – year: 1990 ident: 10.1016/j.nonrwa.2024.104269_b44 |
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| Snippet | We study the anisotropic Forchheimer-typed flows for compressible fluids in porous media. The first half of the paper is devoted to understanding the nonlinear... |
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| SubjectTerms | Anisotropic First-order system Fluid flows Forchheimer Monotonicity Nonlinear partial differential equations Porous media |
| Title | Anisotropic flows of Forchheimer-type in porous media and their steady states |
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