Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions

Journal des Mathematiques Pures et Appliquees

Volumn 77, Issue 4, 1998, Pages 317-354

  Payne, L E ^a   Straughan, B ^b  

^a Department of Obstetrics Gynecology   (United States)

^b The University   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032044524     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(98)80102-5     Document Type: Article

References (30)

1. K. A. AMES and L. E. PAYNE, Continuous dependence results for solutions of the Navier-Stokes equations backward in time. Nonlinear Anal., Theory, Meths., Appl., 23. 1994a, pp. 103-113.
2. K. A. AMES and L. E. PAYNE, On stabilizing against modeling errors in a penetrative convection problem for a porous medium. Math. Models Meth. Appl. Sci. 4. 1994b, pp. 733-740.
3. K. A. AMES and L. E. PAYNE, Continuous dependence results for a problem in penetrative convection. Quart. Appl. Math., 1997a, to appear.
4. K. A. AMES and L. E. PAYNE, Asymptotic behavior for two regularisations of the Cauchy problem for the backward heat equation. Math. Models Meth. Appl. Sci., 1997b, to appear.
5. G. S. BEAVERS and D. D. JOSEPH, Boundary conditions at a naturally impermeable wall. J. Fluid Mech., 30, 1967, pp. 197-207.
6. A. D. BENNETT, Continuous Dependence on Modeling in the Cauchy Problem for Second Order Nonlinear Partial Differential Equations. Ph. D. thesis. Cornell University, 1986.
7. A. D. BENNETT, Continuous dependence on modeling in the Cauchy problem for elliptic equations. Diff. Integral Equations, 4, 1991, pp. 1311-1324.
8. H. DARCY, Les fontaines publiques de la ville de Dijon. Dalmont, Paris, 1856.
9. F. FRANCHI and B. STRAUGHAN, Continuous dependence on the body force for solutions to the Navier-Stokes equations and on the heat supply in a model for double diffusive porous convection. J. Math. Anal. Appl., 172, 1993, pp. 117-129.
10. F. FRANCHI and B. STRAUGHAN, Continuous dependence on the relaxation time and modelling, and unbounded growth, in theories of heat conduction with finite propagation speeds. J. Math. Anal. Appl., 185, 1994a, pp. 726-746.
11. F. FRANCHI and B. STRAUGHAN, Spatial decay estimates and continuous dependence on modelling for an equation from dynamo theory. Proc. Roy. Soc. London A, 445, 1994b, pp. 437-451.
12. F. FRANCHI and B. STRAUGHAN, Structural stability for the Brinkman equations of porous media. Math. Meth. Appl. Sci. 19, 1996, pp. 1335-1347.
13. J. Guo and P. N. KALONI, Nonlinear stability problem of a rotating doubly diffusive porous layer. J. Math. Anal. Appl., 190, 1995a, pp. 373-390.
14. J. Guo and P. N. KALONI, Doubly diffusive convection in a porous medium, nonlinear stability, and the Brinkman effect. Stud. Appl. Math., 94, 1995b, pp. 341-358.
15. I. P. JONES, Low Reynolds number flow past a porous spherical shell. Proc. Camb. Phil. Soc. 73, 1973, pp. 231-238.
16. C. LIN and L. E. PAYNE, On the spatial decay of ill-posed parabolic problems. Math. Models Meth. Appl. Sci., 3, 1993, pp. 563-575.
17. C. LIN and L. E. PAYNE, The influence of domain and diffusivity perturbations on the decay of end effects in heat conduction. SIAM J. Math. Anal., 25, 1994, pp. 1242-1258.
18. G. MCKAY and B. STRAUGHAN, Patterned ground formation under water. Continuum Mech. Thermodyn., 5. 1993, pp. 145-162.
19. A. MORRO and B. STRAUGHAN, Continuous dependence on the source parameters for convective motion in porous media. Nonlinear Analysis, Theory. Meths., Appl., 18, 1992, pp. 307-315.
20. D. A. NIELD, Onset of convection in a fluid layer overlying a layer of porous medium. J. Fluid Mech., 81, 1977, pp. 513-522.
21. D. A. NIELD and A. BEJAN, Convection in Porous Media., Springer-Verlag, New York, 1992.
22. L. E. PAYNE, On stabilizing ill-posed problems against errors in geometry and modeling. Proc. Conf. on Inverse and Ill-posed Problems: Strobhl., H. Engel und C. W. Groetsch (eds.) 1987a, pp. 399-416. Academic Press, New York.
23. L. E. PAYNE, On geometric and modeling perturbations in partial differential equations. In Proc. L.M.S. Symp. on Non-Classical Continuum Mechanics, Knops, R. J. and Lacey, A. A. (eds.) 1987b, pp. 108-128. Cambridge University Press.
24. L. E. PAYNE and J. C. SONG, Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder. Continuum Mech. Thermodyn., 9, 1997, pp. 175-190.
25. L. E. PAYNE, and B. STRAUGHAN, Comparison of viscous flows backward in time with small data. Int. J. Nonlinear Mech., 24, 1989, pp. 209-214.
26. L. E. PAYNE and B. STRAUGHAN, Error estimates for the temperature of a piece of cold ice, given data on only part of the boundary. Nonlinear Analysis, Theory, Meths., Appl, 14, 1990, pp. 443-452.
27. L. E. PAYNE and B. STRAUGHAN, Stability in the initiai - time geometry problem for the Brinkman and Darcy equations of flow in porous media. J. Math. pures et appl., 75, 1996, pp. 225-271.
28. L. E. PAYNE and H. F. WEINBERGER, New bounds for solutions of second order elliptic partial differential equations. Pacific J. Math., 8, 1958, pp. 551-573.
29. Y. QIN and P. N. KALONI, Creeping flow past a porous spherical shell. Z. Angew. Math. Mech., 73, 1993, pp. 77-84.
30. Y. QIN and P. N. KALONI, Corrective instabilities in anisotropic porous media. Stud. Appl. Math., 91, 1994, pp. 189-204.