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Volumn 14, Issue 3, 2013, Pages 1361-1383

Travelling wave solutions for degenerate pseudo-parabolic equations modelling two-phase flow in porous media

Author keywords

Degenerate; Dynamic capillary pressure; Non linear; Pseudo parabolic equations; Sharp travelling waves

Indexed keywords

DEGENERATE; DEGENERATE CASE; DYNAMIC EFFECTS; HIGHER ORDER TERMS; NON-LINEAR; NON-SMOOTH; PSEUDO-PARABOLIC EQUATIONS; TRAVELLING WAVE SOLUTION; TRAVELLING WAVES;

EID: 84872032116     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2012.10.002     Document Type: Article
Times cited : (65)

References (38)
  • 1
    • 0027881895 scopus 로고
    • Thermodynamic basis of capillary pressure in porous media
    • S.M. Hassanizadeh, and W.G. Gray Thermodynamic basis of capillary pressure in porous media Water Resour. Res. 29 1993 3389 3405
    • (1993) Water Resour. Res. , vol.29 , pp. 3389-3405
    • Hassanizadeh, S.M.1    Gray, W.G.2
  • 2
    • 50149084669 scopus 로고    scopus 로고
    • Dimensional analysis of two-phase flow including a rate-dependent capillary pressure-saturation relationship
    • S. Manthey, S.M. Hassanizadeh, R. Helmig, and R. Hilfer Dimensional analysis of two-phase flow including a rate-dependent capillary pressure-saturation relationship Adv. Water Res. 31 2008 1137 1150
    • (2008) Adv. Water Res. , vol.31 , pp. 1137-1150
    • Manthey, S.1    Hassanizadeh, S.M.2    Helmig, R.3    Hilfer, R.4
  • 3
    • 83455218430 scopus 로고    scopus 로고
    • Dynamic effect in the capillary pressure-saturation relationship and its impact on unsaturated flow
    • S.M. Hassanizadeh, M. Celia, and H. Dahle Dynamic effect in the capillary pressure-saturation relationship and its impact on unsaturated flow Vadose Zone J. 1 2002 38 57
    • (2002) Vadose Zone J. , vol.1 , pp. 38-57
    • Hassanizadeh, S.M.1    Celia, M.2    Dahle, H.3
  • 4
    • 2442695645 scopus 로고    scopus 로고
    • Experimental measurements of saturation overshoot on infiltration
    • 10.1029/2003WR002670
    • D.A. DiCarlo Experimental measurements of saturation overshoot on infiltration Water Resour. Res. 40 2004 W04215 10.1029/2003WR002670
    • (2004) Water Resour. Res. , vol.40 , pp. 04215
    • Dicarlo, D.A.1
  • 6
    • 40649086967 scopus 로고    scopus 로고
    • A new class of entropy solutions of the Buckley-Leverett equation
    • C.J. van Duijn, L.A. Peletier, and I.S. Pop A new class of entropy solutions of the Buckley-Leverett equation SIAM J. Math. Anal. 39 2007 507 536
    • (2007) SIAM J. Math. Anal. , vol.39 , pp. 507-536
    • Van Duijn, C.J.1    Peletier, L.A.2    Pop, I.S.3
  • 8
    • 75249094418 scopus 로고    scopus 로고
    • A global existence result for the equations describing unsatured flow in porous media with dynamic capillary pressure
    • A. Mikelić A global existence result for the equations describing unsatured flow in porous media with dynamic capillary pressure J. Differential Equations 248 2010 1561 1577
    • (2010) J. Differential Equations , vol.248 , pp. 1561-1577
    • Mikelić, A.1
  • 9
    • 84871267680 scopus 로고    scopus 로고
    • Existence of weak solutions to a degenerate pseudo-parabolic equation modeling two-phase flow in porous media
    • Eindhoven University of Technology
    • C. Cancès, C. Choquet, Y. Fan, I.S. Pop, Existence of weak solutions to a degenerate pseudo-parabolic equation modeling two-phase flow in porous media, CASA Report 10-75, Eindhoven University of Technology, 2010.
    • (2010) CASA Report 10-75
    • C. Cancès1
  • 10
    • 0031282920 scopus 로고    scopus 로고
    • Traveling waves in a convolution model for phase transitions
    • P.W. Bates, P.C. Fife, X. Ren, and X. Wang Traveling waves in a convolution model for phase transitions Arch. Ration. Mech. Anal. 138 1997 105 136
    • (1997) Arch. Ration. Mech. Anal. , vol.138 , pp. 105-136
    • Bates, P.W.1    Fife, P.C.2    Ren, X.3    Wang, X.4
  • 11
    • 0036054752 scopus 로고    scopus 로고
    • Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms
    • L. Malaguti, and C. Marcelli Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms Math. Nachr. 242 2002 148 164
    • (2002) Math. Nachr. , vol.242 , pp. 148-164
    • Malaguti, L.1    Marcelli, C.2
  • 12
    • 0345116415 scopus 로고    scopus 로고
    • Sharp profiles in degenerate and doubly degenerate Fisher-KPP equations
    • L. Malaguti, and C. Marcelli Sharp profiles in degenerate and doubly degenerate Fisher-KPP equations J. Differential Equations 195 2003 471 496
    • (2003) J. Differential Equations , vol.195 , pp. 471-496
    • Malaguti, L.1    Marcelli, C.2
  • 13
    • 84951609574 scopus 로고
    • Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equation
    • F. Sánchez-Garduño, and P.K. Maini Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equation J. Math. Biol. 33 1994 163 192
    • (1994) J. Math. Biol. , vol.33 , pp. 163-192
    • Sánchez-Garduño, F.1    Maini, P.K.2
  • 15
    • 0037138002 scopus 로고    scopus 로고
    • Diffusive-dispersive traveling waves and kinetic relations. I. Nonconvex hyperbolic conservation laws
    • N. Bedjaoui, and P.G. LeFloch Diffusive-dispersive traveling waves and kinetic relations. I. Nonconvex hyperbolic conservation laws J. Differential Equations 178 2002 574 607
    • (2002) J. Differential Equations , vol.178 , pp. 574-607
    • Bedjaoui, N.1    Lefloch, P.G.2
  • 16
    • 0038919593 scopus 로고    scopus 로고
    • Undercompressive shocks in thin film flows
    • A.L. Bertozzi, A. Münch, and M. Shearer Undercompressive shocks in thin film flows Physica D 134 1999 431 464
    • (1999) Physica D , vol.134 , pp. 431-464
    • Bertozzi, A.L.1    Münch, A.2    Shearer, M.3
  • 17
    • 0031508127 scopus 로고    scopus 로고
    • Nonclassical shocks and kinetic relations: Scalar conservation laws
    • B.T. Hayes, and P.G. LeFloch Nonclassical shocks and kinetic relations: scalar conservation laws Arch. Ration. Mech. Anal. 139 1997 1 56
    • (1997) Arch. Ration. Mech. Anal. , vol.139 , pp. 1-56
    • Hayes, B.T.1    Lefloch, P.G.2
  • 18
    • 0000261039 scopus 로고
    • Travelling wave solutions of the modified Korteweg de Vries-Burgers equation
    • D. Jacobs, B. McKinney, and M. Shearer Travelling wave solutions of the modified Korteweg de Vries-Burgers equation J. Differential Equations 116 1995 448 467
    • (1995) J. Differential Equations , vol.116 , pp. 448-467
    • Jacobs, D.1    McKinney, B.2    Shearer, M.3
  • 19
    • 21344472981 scopus 로고    scopus 로고
    • On undercompressive shocks and flooding in countercurrent two-layer flows
    • T.M. Segin, B.S. Tilley, and L. Kondic On undercompressive shocks and flooding in countercurrent two-layer flows J. Fluid Mech. 532 2005 217 242
    • (2005) J. Fluid Mech. , vol.532 , pp. 217-242
    • Segin, T.M.1    Tilley, B.S.2    Kondic, L.3
  • 20
    • 70349322676 scopus 로고    scopus 로고
    • A kinetic decomposition for singular limits of non-local conservation laws
    • F. Kissling, P.G. LeFloch, and C. Rohde A kinetic decomposition for singular limits of non-local conservation laws J. Differential Equations 247 2009 3338 3356
    • (2009) J. Differential Equations , vol.247 , pp. 3338-3356
    • Kissling, F.1    Lefloch, P.G.2    Rohde, C.3
  • 21
    • 33144489184 scopus 로고    scopus 로고
    • Scalar conservation laws with mixed local and non-local diffusion-dispersion terms
    • C. Rohde Scalar conservation laws with mixed local and non-local diffusion-dispersion terms SIAM J. Math. Anal. 37 2005 103 129
    • (2005) SIAM J. Math. Anal. , vol.37 , pp. 103-129
    • Rohde, C.1
  • 23
    • 0347467589 scopus 로고    scopus 로고
    • Infiltration in porous media with dynamic capillary pressure: Travelling waves
    • C. Cuesta, C.J. van Duijn, and J. Hulshof Infiltration in porous media with dynamic capillary pressure: travelling waves European J. Appl. Math. 11 2000 381 397
    • (2000) European J. Appl. Math. , vol.11 , pp. 381-397
    • Cuesta, C.1    Van Duijn, C.J.2    Hulshof, J.3
  • 25
    • 13844314845 scopus 로고    scopus 로고
    • Dynamic capillary pressure mechanism for instability in gravity-driven flows; Review and extension to very dry conditions
    • J.L. Nieber, R.Z. Dautov, A.G. Egorov, and A.Y. Sheshukov Dynamic capillary pressure mechanism for instability in gravity-driven flows; review and extension to very dry conditions Transp. Porous Media 58 2005 147 172
    • (2005) Transp. Porous Media , vol.58 , pp. 147-172
    • Nieber, J.L.1    Dautov, R.Z.2    Egorov, A.G.3    Sheshukov, A.Y.4
  • 26
    • 63249103861 scopus 로고    scopus 로고
    • Stability analysis of a phase-field model of gravity-driven unsaturated flow through porous media
    • L. Cueto-Felgueroso, and R. Juanes Stability analysis of a phase-field model of gravity-driven unsaturated flow through porous media Phys. Rev. E 79 2009 036301
    • (2009) Phys. Rev. e , vol.79 , pp. 036301
    • Cueto-Felgueroso, L.1    Juanes, R.2
  • 27
    • 33750170480 scopus 로고    scopus 로고
    • Small and waiting-time behavior of a Darcy flow model with a dynamic pressure saturation relation
    • J.R. King, and C.M. Cuesta Small and waiting-time behavior of a Darcy flow model with a dynamic pressure saturation relation SIAM J. Appl. Math. 66 2006 1482 1511
    • (2006) SIAM J. Appl. Math. , vol.66 , pp. 1482-1511
    • King, J.R.1    Cuesta, C.M.2
  • 28
    • 33947163411 scopus 로고    scopus 로고
    • Degenerate quaslinear pseudoparabolic equations with memory terms and variational inequalities
    • M. Ptashnyk Degenerate quaslinear pseudoparabolic equations with memory terms and variational inequalities Nonlinear Anal. 66 2007 2653 2675
    • (2007) Nonlinear Anal. , vol.66 , pp. 2653-2675
    • Ptashnyk, M.1
  • 29
    • 33746807692 scopus 로고    scopus 로고
    • Some qualitative properties of solutions to a pseudoparabolic equation modeling solvent uptake in polymeric solids
    • W. Düll Some qualitative properties of solutions to a pseudoparabolic equation modeling solvent uptake in polymeric solids Comm. Partial Differential Equations 31 2006 1117 1138
    • (2006) Comm. Partial Differential Equations , vol.31 , pp. 1117-1138
    • Düll, W.1
  • 30
    • 67749088283 scopus 로고    scopus 로고
    • Analysis of model equations for stress-enhanced diffusion in coal layers. I. Existence of a weak solution
    • A. Mikelić, and H. Bruining Analysis of model equations for stress-enhanced diffusion in coal layers. I. Existence of a weak solution SIAM J. Math. Anal. 40 2008 1671 1691
    • (2008) SIAM J. Math. Anal. , vol.40 , pp. 1671-1691
    • Mikelić, A.1    Bruining, H.2
  • 31
    • 82555168232 scopus 로고    scopus 로고
    • A class of pseudo-parabolic equations: Existence, uniqueness of weak solutions, and error estimates for the Euler-implicit discretization
    • Y. Fan, and I.S. Pop A class of pseudo-parabolic equations: existence, uniqueness of weak solutions, and error estimates for the Euler-implicit discretization Math. Methods Appl. Sci. 34 2011 2329 2339
    • (2011) Math. Methods Appl. Sci. , vol.34 , pp. 2329-2339
    • Fan, Y.1    Pop, I.S.2
  • 32
    • 0001217997 scopus 로고
    • The Cauchy problem and boundary value problems for equations of the type of unsteady filtration
    • O.A. Oleinik, A.S. Kalashnikov, and Y.L. Zhou The Cauchy problem and boundary value problems for equations of the type of unsteady filtration Izv. Akad. Nauk SSSR Ser. Mat. 22 1958 667 704
    • (1958) Izv. Akad. Nauk SSSR Ser. Mat. , vol.22 , pp. 667-704
    • Oleinik, O.A.1    Kalashnikov, A.S.2    Zhou, Y.L.3
  • 33
    • 0035982250 scopus 로고    scopus 로고
    • A numerical approach to degenerate parabolic equations
    • I.S. Pop, and W. Yong A numerical approach to degenerate parabolic equations Numer. Math. 92 2002 357 381
    • (2002) Numer. Math. , vol.92 , pp. 357-381
    • Pop, I.S.1    Yong, W.2
  • 34
    • 56449111078 scopus 로고    scopus 로고
    • Numerical schemes for a pseudo-parabolic Burgers equation: Discontinuous data and long-time behaviour
    • C.M. Cuesta, and I.S. Pop Numerical schemes for a pseudo-parabolic Burgers equation: discontinuous data and long-time behaviour J. Comput. Appl. Math. 224 2009 269 283
    • (2009) J. Comput. Appl. Math. , vol.224 , pp. 269-283
    • Cuesta, C.M.1    Pop, I.S.2
  • 35
    • 40649093135 scopus 로고    scopus 로고
    • Dynamic capillary effects in heterogeneous porous media
    • R. Helmig, A. Weiss, and B. Wohlmuth Dynamic capillary effects in heterogeneous porous media Comput. Geosci. 11 2007 261 274
    • (2007) Comput. Geosci. , vol.11 , pp. 261-274
    • Helmig, R.1    Weiss, A.2    Wohlmuth, B.3
  • 36
    • 84904822872 scopus 로고    scopus 로고
    • Equivalent formulations and numerical schemes for a class of pseudo-parabolic equations
    • Y. Fan, I.S. Pop, Equivalent formulations and numerical schemes for a class of pseudo-parabolic equations, J. Comput. Appl. Math. (in press). http://dx.doi.org/10.1016/j.cam.2012.07.031.
    • J. Comput. Appl. Math. (In Press)
    • Fan, Y.1    Pop, I.S.2
  • 37
    • 56649088279 scopus 로고    scopus 로고
    • Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media
    • M. Peszyńska, and S. Yi Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media Int. J. Numer. Anal. Model. 5 2008 126 149
    • (2008) Int. J. Numer. Anal. Model. , vol.5 , pp. 126-149
    • Peszyńska, M.1    Yi, S.2
  • 38
    • 0037290482 scopus 로고    scopus 로고
    • A model problem for groundwater flow with dynamic capillary pressure: Stability of traveling waves
    • C. Cuesta, and J. Hulshof A model problem for groundwater flow with dynamic capillary pressure: stability of traveling waves Nonlinear Anal. 52 2003 1199 1218
    • (2003) Nonlinear Anal. , vol.52 , pp. 1199-1218
    • Cuesta, C.1    Hulshof, J.2


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