Convergence of the equations for a Maxwell fluid

Studies in Applied Mathematics

Volumn 103, Issue 3, 1999, Pages 267-278

  Payne, L E ^a   Straughan, B ^b  

^a Department of Obstetrics Gynecology   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

MAXWELL EQUATIONS; VISCOELASTICITY;

LINEAR APPROXIMATIONS; MAXWELL FLUID; MAXWELL'S SYSTEM; PRIORI BOUNDS; STOKES FLOWS; VIS-COELASTIC FLUIDS; VISCO-ELASTIC FLUID;

RELAXATION TIME;

EID: 0039530431     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9590.00128     Document Type: Article

References (26)

1. K. A. AMES and B. STRAUGHAN, Non-Standard and Improperly Posed Problems, Vol. 194, Mathematics in Science and Engineering Series, Academic Press, San Diego, 1997.
2. N. BELLOMO and L. PREZIOSI, Modelling Mathematical Methods and Scientific Computation, CRC Press, Boca Raton, 1995.
3. J. N. FLAVIN and S. RIONERO, Qualitative Estimates for Partial Differential Equations, CRC Press, Boca Raton, 1995.
4. A. D. BENNETT, Continuous dependence on modeling in the Cauchy problem for elliptic equations. Differential and Integral Equations 4:1311-1324 (1991).
5. K. A. AMES and L. E. PAYNE, On stabilizing against modeling errors in a penetrative convection problem for a porous medium, Math. Models Methods Appl. Sci. 4:733-740 (1994).
6. K. A. AMES and L. E. PAYNE, Continuous dependence results for a problem in penetrative convection, Quart. Appl. Math 55:769-790 (1997).
7. K. A. AMES and L. E. PAYNE, Asymptotic behavior for two regularizations of the Cauchy problem for the backward heat equation, Math. Models Methods Appl. Sci. 8:187-202 (1998).
8. S. CHIRITA and S. RIONERO, Lagrange identity in linear viscoelasticity, Int. J. Eng. Sci. 29:1181-1200 (1991).
9. S. RIONERO and S. CHIRITA, New reciprocal and continuous dependence theorems in the linear theory of viscoelasticity, Int. J. Eng. Sci. 27:1023-1036 (1989).
10. 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. 25:1242-1258 (1994).
11. L. E. PAYNE and B. STRAUGHAN, Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions, J. Math. Pures et Appl. 77:317-354 (1998).
12. L. E. PAYNE and B. STRAUGHAN, Structural stability for the Darcy equations of flow in porous media, Proc. Roy. Soc. London A 454:1691-1698 (1998).
13. L. E. PAYNE and B. STRAUGHAN, Convergence and continuous dependence for the Brinkman-Forchheimer equations, Stud. Appl. Math., 102:419-439 (1999).
14. B. STRAUGHAN and K. HUTTER, A priori bounds and structural stability for double diffusive convection incorporating the Soret effect, Proc. Roy. Soc. London A: 455:767-777 (1999).
15. Y. QIN and P. N. KALONI, Convective instabilities in anisotropic porous media, Stud. Appl. Math. 91:189-204 (1994).
16. B. STRAUGHAN and D. W. WALKER, Anisotropic porous penetrative convection, Proc. Roy. Soc. London A 452:97-115 (1996).
17. Y. QIN and J. CHADAM, Nonlinear convective stability in a porous medium with temperature-dependent viscosity and inertial drag, Stud. Appl. Math. 96:273-288 (1996).
18. J. Guo and P. N. KALONI, Doubly diffusive convection in a porous medium, nonlinear stability, and the Brinkman effect, Stud. Appl. Math. 94:341-358 (1995).
19. P. N. KALONI and J. Guo, Steady nonlinear double-diffusive convection in a porous medium based upon the Brinkman-Forchheimer model, J. Math. Anal. Appl. 204:138-155 (1996).
20. Y. QIN and P. N. KALONI, Spatial decay estimates for plane flow in the Brinkman-Forchheimer model, Quart. Appl. Math. 56:71-87 (1998).
21. L. E. PAYNE and J. C. SONG, Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder, Continuum Mech. Thermodynamics 9:175-190 (1997).
22. L. E. PAYNE and B. STRAUGHAN, Stability in the initial-time geometry problem for the Brinkman and Darcy equations of flow in porous media, J. Math. Pures et Appl. 75:225-271 (1996).
23. M. LÖPEZ DE HARO, P. J. A. DEL RIO AND S. WHITAKER, Flow of Maxwell fluids in porous media, Transport in Porous Media 25:167-192 (1996).
24. C. R. DOERING and J. D. GIBBON, Applied Analysis of the Navier-Stokes Equations, Cambridge University Press, Cambridge, 1995.
25. B. STRAUGHAN, The Energy Method, Stability, and Nonlinear Convection, Springer, BerlinHeidelberg, 1992.
26. B. STRAUGHAN, Explosive Instabilities in Mechanics, Springer, Berlin-Heidelberg, 1998.