A model problem for groundwater flow with dynamic capillary pressure: Stability of travelling waves

Nonlinear Analysis, Theory, Methods and Applications

Volumn 52, Issue 4, 2003, Pages 1199-1218

  Cuesta, Carlota ^a   Hulshof, J ^a  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Dynamic capillary pressure; Stability; Travelling waves; Unsaturated flow

Indexed keywords

CAPILLARY FLOW; DIFFUSION IN LIQUIDS; LINEAR EQUATIONS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PRESSURE EFFECTS;

DYNAMIC CAPILLARY PRESSURE;

GROUNDWATER FLOW;

EID: 0037290482     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(02)00160-8     Document Type: Article

References (16)

1. Barenblatt G.I., García-Azorero J., De Pablo A., Vázquez J.L. Mathematical model of the non-equilibrium water-oil displacement in porous strata. Applicable Anal. 65:1997;19-45.
2. Barenblatt G.I., Entov V.M., Ryzhik V.M. Theory of Fluid Flow Through Natural Rocks. 1990;Kluwer, Dordrecht-Boston-London.
3. Bourgeat A., Panfilov M. Effective two-phase flow through highly heterogeneous porous media. capillary nonequilibrium effects Computat. Geosci. 2:1998;191-215.
4. H. Brezis, Analyse fonctionnelle: theorie et applications, Masson, 1983.
5. Cuesta C., van Duijn C.J., Hulshof J. Infiltration in porous media with dynamic capillary pressure. travelling waves Euro. J. Appl. Math. 11:2000;381-397.
6. DiBenedetto E., Pierre M. On the maximum principle for pseudoparabolic equations. Indiana Univ. Math. J. 30:1981;821-854.
7. S.M. Hassanizadeh, Dynamic effects in the capillary pressure saturation relationship, Proceedings of 4th International Conference on Civil Engineering, Vol. 4, Water Resources and Environment Engineering, Sharif U. of Technology, Tehran, May 1997, pp. 141-149.
8. Hassanizadeh S.M., Gray W.G. Thermodynamic basis of capillary pressure in porous media. Water Resources Res. 29:1993;3389-3405.
9. S.M. Hassanizadeh, R.J. Schotting, A. Yu Beliaev, A new capillary pressure-saturation relationship including hysteresis and dynamic effects, in: Bentley et al. (Eds), Proceedings of the XIII International Conference on Computational Methods in Water Resources, Balkema Rotterdam, Calgary, Canada, June 2000, pp. 245-251.
10. xx Comm. Pure Appl. Math. 3:1950;201-230.
11. Hulshof J., King J.R. Analysis of a Darcy flow model with a dynamic pressure saturation relation. SIAM J. Appl. Math. 59(1):1998;318-346.
12. Il'in A.M., Oleinik O.A. Behaviour of the solutions of the Cauchy problem for certain quasilinear equations for unbounded increase of the time. Amer. Math. Soc. Translations Ser. 2. 42:1964;19-23.
13. Pego R.L. Remarks on the stability of shock profiles for conservation laws with dissipation. Trans. Amer. Math Soc. 291:1985;353-361.
14. Pego R.L., Smereka P., Weinstein M.I. Oscillatory instability of travelling waves for Kdv-Burgers equation. Physica D. 67:1993;45-65.
15. F. Stauffer, Time dependence of the relations between capillary pressure, water content and conductivity during drainage of porous media, LAHR Symposium on Scale Effects in Porous Media, Thessaloniki, Greece, August 29-September 1, 1978.
16. Visintin A. Differential Models of Hysteresis. 1994;Springer, New York.