Effect of errors in the spatial geometry for temperature dependent stokes flow

Journal des Mathematiques Pures et Appliquees

Volumn 78, Issue 6, 1999, Pages 609-632

  Payne, L E ^a   Straughan, B ^b  

^a Department of Obstetrics Gynecology   (United States)

^b Department of Mathematics   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033147434     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(99)00011-2     Document Type: Article

References (30)

1. K. A. Ames and L.E. Payne, Stabilizing the backward heat equation against errors in the initial time geometry, Inequalities and Applications 3 (1994) 47-52.
2. K.A. Ames and L.E. Payne, Continuous dependence on initial-time geometry for a thermoelastic system with sign-indefinite elasticities, J. Math. Anal. Appl. 189 (1995) 693-714.
3. K.A. Ames and B. Straughan, Estimates of the error in the initial-time geometry for a parabolic equation from dynamo theory, J. Differential Equations 123 (1995) 153-170.
4. K.A. Ames and B. Straughan, Non-Standard and Improperly Posed Problems, Mathematics in Science and Engineering Series, Vol. 194, Academic Press, San Diego, 1997.
5. P.S. Crooke and L.E. Payne, Continuous dependence on geometry for the backward heat equation, Math. Meth. Appl. Sci. 6 (1984) 433-448.
6. J.N. Flavin and S. Rionero, Qualitative Estimates for Partial Differential Equations, CRC Press, Boca Raton, 1995.
7. F. Franchi and B. Straughan, Effects of errors in the initial-time geometry on the solution of an equation from dynamo theory in an exterior domain, Proc. Roy. Soc. London A 450 (1995) 109-121.
8. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977.
9. J. Hersch and L.E. Payne, Extremal principles and isoperimetric inequalities for some mixed problems of Stekloff's type, ZAMP 19 (1968) 802-817.
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 (1994) 1242-1258.
11. L.E. Payne, Isoperimetric inequalities and their applications, SIAM Review 9 (1967) 453-488.
12. L.E. Payne, Bounds for the maximum stress in the St. Venant torsion problem, Indian Journal of Math. Mech. (Special Issue), 1968, pp. 51-59.
13. L.E. Payne, On stabilizing ill-posed problems against errors in geometry and modeling, in: Strobhl, H. Engel and C.W. Groetsch (Eds.), Proc. Conf. on Inverse and Ill-Posed Problems: Academic Press, New York, 1987, pp. 399-416.
14. L.E. Payne, On geometric and modeling perturbations in partial differential equations, in: R.J. Knops and A.A. Lacey (Eds.), Proc. LMS Symp. on Non-Classical Continuum Mechanics, Cambridge University Press, 1987, pp. 108-128.
15. L.E. Payne, Some special maximum principles with applications to isoperimetric inequalities, in: P.W. Schaefer (Ed.), Maximum Principles and Eigenvalue Problems in Partial Differential Equations, Pitman Research Notes in Mathematics 175, Longman, 1988, pp. 15-33.
16. L.E. Payne, Continuous dependence on geometry with applications in continuum mechanics, in: G.A.C. Graham and S.K. Malik (Eds.), Continuum Mechanics and its Applications, Hemisphere Publ. Co., 1989, pp. 877-890.
17. L.E. Payne, Some remarks on ill-posed problems for viscous fluids, Int. J. Engng. Sci. 30 (1992) 1341-1347.
18. L.E. Payne, Continuous dependence on spatial geometry for solutions of the Navier-Stokes equations backward in time, Nonlinear Anal., Theory, Meths., Applicns. 21 (1993) 651-664.
19. L.E. Payne and J.C. Song, Continuous dependence on initial-time and spatial geometry in generalised heat conduction, J. Math. Anal. Appl. 214 (1997) 173-190.
20. L.E. Payne and J.C. Song, Continuous dependence on the initial-time geometry in generalised heat conduction, Math. Models Meth. Appl. Sci. 7 (1997) 125-138.
21. 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 (1996) 225-271.
22. 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 (1998) 317-354.
23. L.E. Payne and B. Straughan, Structural stability for the Darcy equations of flow in porous media, Proc. Roy. Soc. London A 454 (1998) 1691-1698.
24. L.E. Payne and H.F. Weinberger, New bounds for solutions of second order elliptic partial differential equations, Pacific J. Math. 8 (1958) 551-573.
25. J. Persens, On Stabilizing Ill-Posed Problems for Partial Differential Equations under Perturbations of the Geometry of the Domain, Ph.D. Thesis, Cornell University, 1986.
26. J.N. Reddy, An Introduction to the Finite Element Method, McGraw-Hill, 1984.
27. V.G. Sigillito, Explicit a Priori Inequalities with Applications to Boundary Value Problems, Pitman Res. Notes Math., 13, Pitman Press, London, 1977.
28. J.C. Song, Some Stability Criteria in Fluid and Solid Mechanics, Ph.D. Thesis, Cornell University, 1988.
29. B. Straughan, The energy method, stability, and nonlinear convection, Appl. Math. Sci. Ser., Vol. 91, Springer, Berlin, 1992.
30. B. Straughan, Explosive Instabilities in Mechanics, Physics Series, Springer, Berlin, 1998.