A singular perturbation problem in fractured media with parallel diffusion

Mathematical Models and Methods in Applied Sciences

Volumn 8, Issue 4, 1998, Pages 645-655

  Logan, J David ^a   Ledder, Glenn ^a   Homp, Michelle Reeb ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b Department of Applied Human Sciences   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032329710     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202598000299     Document Type: Article

References (20)

1. J. D. Buckmaster, An introduction to combustion theory, in The Mathematics of Combustion, ed. J. D. Buckmaster (SIAM, 1985).
2. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Clarendon Press, 1959).
3. C. S. Chen, Solutions for radionuclide transport from an injection well into a single fracture in a porous formation, Water Resour. Res. 22 (1986) 508-518.
4. R. V. Churchill, Operational Mathematics (McGraw-Hill, 1972), 3rd edition.
5. A. Fogden, K. A. Landman and L. R. White, Contaminant transport in fractured media: steady state solutions by a boundary integral method, Water Resour. Res. 24 (1988) 1384-1396.
6. G. E. Grisak and J. F. Pickens, Solute transport through fractured media, 1, the effect of matrix diffusion, Water Resour. Res. 16 (1980) 719-730.
7. G. E. Grisak and J. F. Pickens, An analytical solution for solute transport through fractured media with matrix diffusion, J. Hydrology 52 (1981) 47-57.
8. M. Homp and J. D. Logan, Contaminant transport in fractured media with sources in the porous domain, Transport Porous Media 29 (1997) 341-353.
9. P. S. Huyakorn, B. H. Lester and J. W. Mercer, 1983. An efficient finite element technique for modeling transport in fractured porous media, 1, single species transport, Water Resour. Res. 19 (1983) 841-854.
10. K. A. Landman, A boundary integral method for contaminant transport in two adjacent porous media, J. Aust. Math. Soc. Ser. B 30 (1989) 251-267.
11. J. D. Logan, V. Zlotnik and S. Cohn, Transport in fractured porous media with time-periodic boundary conditions, Math. Comput. Modelling 24 (1996) 1-9.
12. R. P. Lowell, Contaminant transport in a single fracture: periodic boundary and flow conditions, Water Resour. Res. 25 (1989) 774-780.
13. P. Maloszewski and A. Zuber, On the theory of tracer experiments in fissured rocks with porous matrix, J. Hydrology 79 (1985) 333-358.
14. Mathematica, ver 2.0 (Wolfram Research Inc., 1992).
15. I. Neretnieks, Diffusion in the rock matrix: an important factor in radionuclide retardation? J. Geophys. Res. 85 (1980) 4379-4397.
16. J. Noorishad and M. Mehran, An upstream finite element method for solution of transient transport equations in fractured porous media, Water Resour. Res. 18 (1982) 588-596.
17. E. A. Sudicky and E. O. Frind, Contaminant transport in fractured porous media: analytical solutions for a system of parallel fractures, Water Resour. Res. 18 (1982) 1634-1642.
18. E. A. Sudicky and E. O. Frind, Contaminant transport in fractured porous media: analytical solutions for a two-member decay chain in a single fracture, Water Resour. Res. 20 (1984) 1021-1029.
19. N.-Z. Sun, Mathematical Modeling of Groundwater Pollution (Springer, 1996).
20. D. H. Tang, E. A. Sudicky and E. O. Frind, Contaminant transport in fractured porous media: analytical solution for a single fracture, Water Resour. Res. 17 (1981) 555-564.