Continuous dependence and decay for the Forchheimer equations

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 459, Issue 2040, 2003, Pages 3195-3202

  Franchi, F ^a   Straughan, B ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Continuous dependence; Decay in time; Forchheimer equations; Porous media flows

Indexed keywords

ARTICLE; ENERGY; KINETICS; MATHEMATICAL COMPUTING; STATISTICAL ANALYSIS; STRUCTURE ANALYSIS; VISCOSITY;

EID: 1542407750     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2003.1169     Document Type: Article

References (24)

1. Ames, K. A. & Payne, L. E. 1994 On stabilizing against modeling errors in a penetrative convection problem for a porous medium. Math. Models Meth. Appl. Sci. 4, 733-740.
2. Ames, K. A. & Straughan, B. 1997 Non-standard and improperly posed problems. Academic.
3. Doering, C. R. & Constantin, P. 1998 Bounds for heat transport in a porous layer. J. Fluid Mech. 376, 263-296.
4. Doering, C. R. & Gibbon, J. D. 1995 Applied analysis of the Navier-Stokes equations. Cambridge University Press.
5. Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic stability. Cambridge University Press.
6. Firdaouss, M., Guermond, J. L. & Le Quére, P. 1997 Nonlinear corrections to Darcy's law at low Reynolds numbers. J. Fluid Mech. 343, 331-350.
7. Flavin, J. N. & Rionero, S. 1995 Qualitative estimates for partial differential equations. Boca Raton, FL: CRC Press.
8. Franchi, F. 1994 Stabilization estimates for penetrative motions in porous media. Math. Meth. Appl. Sci. 17, 11-20.
9. Franchi, F. & Straughan, B. 1993 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. Analysis Applic. 172, 117-129.
10. Franchi, F. & Straughan, B. 1994a Spatial decay estimates and continuous dependence on modelling for an equation from dynamo theory. Proc. R. Soc. Lond. A 445, 437-451.
11. Franchi, F. & Straughan, B. 1994b Structural stability for the Brinkman equations of porous media. Math. Math. Appl. Sci. 19, 1335-1347.
12. Giorgi, T. 1997 Derivation of the Forchheimer law via matched asymptotic expansions. Transport Porous Media 29, 191-206.
13. Néel, M. C. 1998 Convection forcée en milieu poreux: écarts à la loi de Darcy. C. R. Acad. Sci. Paris Sér. IIb 326, 615-620.
14. Nield, D. A. & Bejan, A. 1999 Convection in porous media. Springer.
15. Payne, L. E. & Straughan, B. 1998a Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions. J. Math. Pures Appl. 77, 317-354.
16. Payne, L. E. & Straughan, B. 1998b Structural stability for the Darcy equations of flow in porous media. Proc. R. Soc. Lond. A 454, 1691-1698.
17. Payne, L. E. & Straughan, B. 1999 Convergence, continuous dependence and decay for the Brinkman-Forchheimer equations. Stud. Appl. Math. 102, 419-439.
18. Payne, L. E. & Straughan, B. 2000 Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium. Stud. Appl. Math. 105, 59-81.
19. Payne, L. E., Song, J. C. & Straughan, B. 1999 Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity. Proc. R. Soc. Lond. A 455, 2173-2190.
20. Payne, L. E., Rodrigues, J. F. & Straughan, B. 2000 Effect of anisotropic permeability on Darcy's law. Math. Meth. Appl. Sci. 24, 427-438.
21. Qin, Y. & Chadam, J. 1996 Nonlinear convective stability in a porous medium with temperature-dependent viscosity and inertial drag. Stud. Appl. Math. 96, 273-288.
22. Straughan, B. 2001 A sharp nonlinear stability threshold in rotating porous convection. Proc. R. Soc. Lond. A 457, 87-93.
23. Straughan, B. & Hutter, K. 1999 A priori bounds and structural stability for double diffusive convection incorporating the Soret effect. Proc. R. Soc. Lond. A 455, 767-777.
24. Whitaker, S. 1996 The Forchheimer equation: a theoretical development. Transport Porous Media 25, 27-62.