-
Previous Article
From particles scale to anomalous or classical convection-diffusion models with path integrals
- DCDS-S Home
- This Issue
-
Next Article
Preface: Workshop in fluid mechanics and population dynamics
Study of degenerate parabolic system modeling the hydrogen displacement in a nuclear waste repository
1. | CEA Saclay, DEN/DANS/DM2S/SFME/LSET5, 91191 Gif Sur Yvette, France |
2. | King Abdullah University of Science and Technology (KAUST), Computer, Electrical and Mathematical Sciences & Engineering, 23955-6900, Thuwal, Saudi Arabia |
3. | Ecole Centrale de Nantes, Département d' Informatique et Mathématiques, Laboratoire de Mathématiques Jean Leray (UMR 6629 CNRS), 1, rue de la Noé, BP 92101, France |
References:
[1] |
H. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z., 3 (1983), 311-341.
doi: 10.1007/BF01176474. |
[2] |
B. Amaziane, S. Antontsev, L. Pankratov and A. Piatnitski, Homogenization of immiscible compressible two-phase flow in porous media: Application to gas migration in a nuclear waste repository, Multiscale Modeling and Simulation, 8 (2010), 2023-2047.
doi: 10.1137/100790215. |
[3] |
B. Amaziane and M. Jurak, Formulation of immiscible compressible two-phase flow in porous media, Comptes Rendus Mécanique, 7 (2008), 600-605.
doi: 10.1016/j.crme.2008.04.008. |
[4] |
B. Andreianov, M. Bendahmane, K. H. Karlsen and S. Ouaro, Well-posedness results for triply nonlinear degenerate parabolic equations, Journal of Differential Equations, 247 (2009), 277-302.
doi: 10.1016/j.jde.2009.03.001. |
[5] |
M. Bendahmane and K. H. Karlsen, Renormalized entropy solutions for quasi-linear anisotropic degenerate parabolic equations, SIAM J. Math. Anal., 36 (2004), 405-422.
doi: 10.1137/S0036141003428937. |
[6] |
A. Bourgeat, M. Jurak and F. Smai, Two-phase, partially miscible flow and transport modeling in porous media; application to gaz migration in a nuclear waste repository, Computational Geosciences, 4 (2009), 309-325. |
[7] |
F. Caro, B. Saad and M. Saad, Two-component two-compressible flow in a porous medium, Acta Applicandae Mathematicae, 117 (2012), 15-46.
doi: 10.1007/s10440-011-9648-0. |
[8] |
G. Chavent and J. Jaffré, "Mathematical Models and Finite Elements for Reservoir Simulation: Single Phase, Multiphase, and Multicomponent Flows through Porous Media," Studies in Mathematics and its Applications, Elsevier, 1986. |
[9] |
Z. Chen, Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution, Journal of Differential Equations, 171 (2001), 203-232.
doi: 10.1006/jdeq.2000.3848. |
[10] |
Z. Chen, Degenerate two-phase incompressible flow. II. Regularity, stability and stabilization, Journal of Differential Equations, 186 (2002), 345-376.
doi: 10.1016/S0022-0396(02)00027-X. |
[11] |
C. Choquet, Asymptotic analysis of a nonlinear parabolic problem modelling miscible compressible displacement in porous media, Nonlinear Differential Equations and Appl., 15 (2008), 757-782.
doi: 10.1007/s00030-008-8010-3. |
[12] |
C. Choquet, On a fully nonlinear parabolic problem modelling miscible compressible displacement in porous media, Journal of Mathematical Analysis and Applications, 339 (2008), 1112-1133.
doi: 10.1016/j.jmaa.2007.07.037. |
[13] |
F. Z. Daïm, R. Eymard and D. Hilhorst, Existence of a solution for two phase flow in porous media: The case that the porosity depends on pressure, Journal of Mathematical Analysis and Applications, 326 (2007), 332-351.
doi: 10.1016/j.jmaa.2006.02.082. |
[14] |
X. Feng, On existence and uniqueness results for a coupled systems modelling miscible displacement in porous media, J. Math. Anal. Appl., 194 (1995), 883-910.
doi: 10.1006/jmaa.1995.1334. |
[15] |
G. Gagneux and M. Madaune-Tort, "Analyse Mathématique de Modèles Non Linéaires de l'Ingéniere Pétrolière," Mathématiques & Applications (Berlin), Vol. 22, Springer-Verlag, Berlin, 1996. |
[16] |
C. Galusinski and M. Saad, A nonlinear degenerate system modelling water-gas flows in porous media, Discrete and Continuous Dynamical System Ser. B, 9 (2008), 281-308. |
[17] |
C. Galusinski and M. Saad, Two compressible immiscible fluids in porous media, J. Differential Equations, 244 (2008), 1741-1783.
doi: 10.1016/j.jde.2008.01.013. |
[18] |
C. Galusinski and M. Saad, Weak solutions for immiscible compressible multifluid flows in porous media, C. R. Acad. Sci. Paris, 347 (2009), 249-254.
doi: 10.1016/j.crma.2009.01.023. |
[19] |
Z. Khalil and M. Saad, Solutions to a model for compressible immiscible two phase flow in porous media, Electronic Journal of Differential Equations, 2010 (2010), 33 pp. |
[20] |
Z. Khalil and M. Saad, On a fully nonlinear degenerate parabolic system modeling immiscible gas-water displacement in porous media, Nonlinear Analysis, 12 (2011), 1591-1615.
doi: 10.1016/j.nonrwa.2010.10.015. |
[21] |
A. Mikelić, An existence result for the equations describing a gas-liquid two-phase flow, Comptes rendus Mécanique, 337 (2009), 226-232. |
[22] |
F. Smaï, A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository, C. R. Acad. Sci. Paris, 347 (2009), 527-532.
doi: 10.1016/j.crma.2009.03.011. |
[23] |
, J. Talandier. Available from: http://www.andra.fr. |
[24] |
E. Zeidler, "Nonlinear Functional Analysis and its Applications. I. Fixed-Point Theorems," Springer-Verlag, New-York, 1993. |
show all references
References:
[1] |
H. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z., 3 (1983), 311-341.
doi: 10.1007/BF01176474. |
[2] |
B. Amaziane, S. Antontsev, L. Pankratov and A. Piatnitski, Homogenization of immiscible compressible two-phase flow in porous media: Application to gas migration in a nuclear waste repository, Multiscale Modeling and Simulation, 8 (2010), 2023-2047.
doi: 10.1137/100790215. |
[3] |
B. Amaziane and M. Jurak, Formulation of immiscible compressible two-phase flow in porous media, Comptes Rendus Mécanique, 7 (2008), 600-605.
doi: 10.1016/j.crme.2008.04.008. |
[4] |
B. Andreianov, M. Bendahmane, K. H. Karlsen and S. Ouaro, Well-posedness results for triply nonlinear degenerate parabolic equations, Journal of Differential Equations, 247 (2009), 277-302.
doi: 10.1016/j.jde.2009.03.001. |
[5] |
M. Bendahmane and K. H. Karlsen, Renormalized entropy solutions for quasi-linear anisotropic degenerate parabolic equations, SIAM J. Math. Anal., 36 (2004), 405-422.
doi: 10.1137/S0036141003428937. |
[6] |
A. Bourgeat, M. Jurak and F. Smai, Two-phase, partially miscible flow and transport modeling in porous media; application to gaz migration in a nuclear waste repository, Computational Geosciences, 4 (2009), 309-325. |
[7] |
F. Caro, B. Saad and M. Saad, Two-component two-compressible flow in a porous medium, Acta Applicandae Mathematicae, 117 (2012), 15-46.
doi: 10.1007/s10440-011-9648-0. |
[8] |
G. Chavent and J. Jaffré, "Mathematical Models and Finite Elements for Reservoir Simulation: Single Phase, Multiphase, and Multicomponent Flows through Porous Media," Studies in Mathematics and its Applications, Elsevier, 1986. |
[9] |
Z. Chen, Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution, Journal of Differential Equations, 171 (2001), 203-232.
doi: 10.1006/jdeq.2000.3848. |
[10] |
Z. Chen, Degenerate two-phase incompressible flow. II. Regularity, stability and stabilization, Journal of Differential Equations, 186 (2002), 345-376.
doi: 10.1016/S0022-0396(02)00027-X. |
[11] |
C. Choquet, Asymptotic analysis of a nonlinear parabolic problem modelling miscible compressible displacement in porous media, Nonlinear Differential Equations and Appl., 15 (2008), 757-782.
doi: 10.1007/s00030-008-8010-3. |
[12] |
C. Choquet, On a fully nonlinear parabolic problem modelling miscible compressible displacement in porous media, Journal of Mathematical Analysis and Applications, 339 (2008), 1112-1133.
doi: 10.1016/j.jmaa.2007.07.037. |
[13] |
F. Z. Daïm, R. Eymard and D. Hilhorst, Existence of a solution for two phase flow in porous media: The case that the porosity depends on pressure, Journal of Mathematical Analysis and Applications, 326 (2007), 332-351.
doi: 10.1016/j.jmaa.2006.02.082. |
[14] |
X. Feng, On existence and uniqueness results for a coupled systems modelling miscible displacement in porous media, J. Math. Anal. Appl., 194 (1995), 883-910.
doi: 10.1006/jmaa.1995.1334. |
[15] |
G. Gagneux and M. Madaune-Tort, "Analyse Mathématique de Modèles Non Linéaires de l'Ingéniere Pétrolière," Mathématiques & Applications (Berlin), Vol. 22, Springer-Verlag, Berlin, 1996. |
[16] |
C. Galusinski and M. Saad, A nonlinear degenerate system modelling water-gas flows in porous media, Discrete and Continuous Dynamical System Ser. B, 9 (2008), 281-308. |
[17] |
C. Galusinski and M. Saad, Two compressible immiscible fluids in porous media, J. Differential Equations, 244 (2008), 1741-1783.
doi: 10.1016/j.jde.2008.01.013. |
[18] |
C. Galusinski and M. Saad, Weak solutions for immiscible compressible multifluid flows in porous media, C. R. Acad. Sci. Paris, 347 (2009), 249-254.
doi: 10.1016/j.crma.2009.01.023. |
[19] |
Z. Khalil and M. Saad, Solutions to a model for compressible immiscible two phase flow in porous media, Electronic Journal of Differential Equations, 2010 (2010), 33 pp. |
[20] |
Z. Khalil and M. Saad, On a fully nonlinear degenerate parabolic system modeling immiscible gas-water displacement in porous media, Nonlinear Analysis, 12 (2011), 1591-1615.
doi: 10.1016/j.nonrwa.2010.10.015. |
[21] |
A. Mikelić, An existence result for the equations describing a gas-liquid two-phase flow, Comptes rendus Mécanique, 337 (2009), 226-232. |
[22] |
F. Smaï, A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository, C. R. Acad. Sci. Paris, 347 (2009), 527-532.
doi: 10.1016/j.crma.2009.03.011. |
[23] |
, J. Talandier. Available from: http://www.andra.fr. |
[24] |
E. Zeidler, "Nonlinear Functional Analysis and its Applications. I. Fixed-Point Theorems," Springer-Verlag, New-York, 1993. |
[1] |
Shifeng Geng, Lina Zhang. Large-time behavior of solutions for the system of compressible adiabatic flow through porous media with nonlinear damping. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2211-2228. doi: 10.3934/cpaa.2014.13.2211 |
[2] |
Cédric Galusinski, Mazen Saad. A nonlinear degenerate system modelling water-gas flows in porous media. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 281-308. doi: 10.3934/dcdsb.2008.9.281 |
[3] |
Shifeng Geng, Zhen Wang. Best asymptotic profile for the system of compressible adiabatic flow through porous media on quadrant. Communications on Pure and Applied Analysis, 2012, 11 (2) : 475-500. doi: 10.3934/cpaa.2012.11.475 |
[4] |
Yangyang Qiao, Huanyao Wen, Steinar Evje. Compressible and viscous two-phase flow in porous media based on mixture theory formulation. Networks and Heterogeneous Media, 2019, 14 (3) : 489-536. doi: 10.3934/nhm.2019020 |
[5] |
Brahim Amaziane, Leonid Pankratov, Andrey Piatnitski. An improved homogenization result for immiscible compressible two-phase flow in porous media. Networks and Heterogeneous Media, 2017, 12 (1) : 147-171. doi: 10.3934/nhm.2017006 |
[6] |
Bilal Saad, Mazen Saad. Numerical analysis of a non equilibrium two-component two-compressible flow in porous media. Discrete and Continuous Dynamical Systems - S, 2014, 7 (2) : 317-346. doi: 10.3934/dcdss.2014.7.317 |
[7] |
Michiel Bertsch, Danielle Hilhorst, Hirofumi Izuhara, Masayasu Mimura, Tohru Wakasa. A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3117-3142. doi: 10.3934/dcds.2019226 |
[8] |
Brahim Amaziane, Leonid Pankratov, Andrey Piatnitski. The existence of weak solutions to immiscible compressible two-phase flow in porous media: The case of fields with different rock-types. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1217-1251. doi: 10.3934/dcdsb.2013.18.1217 |
[9] |
María Anguiano, Renata Bunoiu. Homogenization of Bingham flow in thin porous media. Networks and Heterogeneous Media, 2020, 15 (1) : 87-110. doi: 10.3934/nhm.2020004 |
[10] |
Cedric Galusinski, Mazen Saad. Water-gas flow in porous media. Conference Publications, 2005, 2005 (Special) : 307-316. doi: 10.3934/proc.2005.2005.307 |
[11] |
Tariel Sanikidze, A.F. Tedeev. On the temporal decay estimates for the degenerate parabolic system. Communications on Pure and Applied Analysis, 2013, 12 (4) : 1755-1768. doi: 10.3934/cpaa.2013.12.1755 |
[12] |
Michiel Bertsch, Roberta Dal Passo, Lorenzo Giacomelli, Giuseppe Tomassetti. A nonlocal and fully nonlinear degenerate parabolic system from strain-gradient plasticity. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 15-43. doi: 10.3934/dcdsb.2011.15.15 |
[13] |
Yuya Tanaka, Tomomi Yokota. Finite-time blow-up in a quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022075 |
[14] |
Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206 |
[15] |
Xian-Gao Liu, Jie Qing. Globally weak solutions to the flow of compressible liquid crystals system. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 757-788. doi: 10.3934/dcds.2013.33.757 |
[16] |
Ting Zhang. The modeling error of well treatment for unsteady flow in porous media. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2171-2185. doi: 10.3934/dcdsb.2015.20.2171 |
[17] |
El Mustapha Ait Ben Hassi, Mohamed Fadili, Lahcen Maniar. Controllability of a system of degenerate parabolic equations with non-diagonalizable diffusion matrix. Mathematical Control and Related Fields, 2020, 10 (3) : 623-642. doi: 10.3934/mcrf.2020013 |
[18] |
Brahim Allal, Abdelkarim Hajjaj, Jawad Salhi, Amine Sbai. Boundary controllability for a coupled system of degenerate/singular parabolic equations. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021055 |
[19] |
Kenneth H. Karlsen, Süleyman Ulusoy. On a hyperbolic Keller-Segel system with degenerate nonlinear fractional diffusion. Networks and Heterogeneous Media, 2016, 11 (1) : 181-201. doi: 10.3934/nhm.2016.11.181 |
[20] |
Andrey Shishkov, Laurent Véron. Propagation of singularities of nonlinear heat flow in fissured media. Communications on Pure and Applied Analysis, 2013, 12 (4) : 1769-1782. doi: 10.3934/cpaa.2013.12.1769 |
2021 Impact Factor: 1.865
Tools
Metrics
Other articles
by authors
[Back to Top]