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Existence et approximation de points selles pour certains problèmes non linéaires. (French) Zbl 0371.65025


MSC:

65Z05 Applications to the sciences
49J20 Existence theories for optimal control problems involving partial differential equations
35J65 Nonlinear boundary value problems for linear elliptic equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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References:

[1] 1. J. P. AUBIN, Cours d’optimisation, Cahiers mathématiques de la décision, Université, Paris-IX, 1972, Approximation of Elliptic Boundary Value Problems, Wiley, Interscience, 1972.
[2] 2. A. BENSOUSSAN, J. L. LIONS et R. TEMAM, Sur les méthodes de décomposition, de coordination, de décentralisations et applications IRIA, Cahier n^\circ 11, t. 2, 1972. Zbl0275.90042 · Zbl 0275.90042
[3] 3. F. BREZZI, Approximation of Saddle Points, R.A.I.R.O., 2, 1974, p. 129-151. Zbl0338.90047 MR365287 · Zbl 0338.90047
[4] 4. F. BREZZI et G. SACCHI, A Finite Element Approximation of a Variational Inequality Related to Hydraulics (à paraître). Zbl0353.76068 · Zbl 0353.76068
[5] 5. I. EKELAND et R. TEMAM, Analyse convexe et problèmes variationnels, Dunod-Bordas, Paris, 1974. English translation : North Holland, Amsterdam, 1975. Zbl0281.49001 MR463993 · Zbl 0281.49001
[6] 6. R. S. FALK, Error Estimates for the Approximation of a Class of Variational Inequalities, Math. of Comp., vol. 28, 1974, p. 963-971. Zbl0297.65061 MR391502 · Zbl 0297.65061
[7] 7. R. GLOWINSKI et A. MARROCO, Sur l’approximation par éléments finis d’ordre 1 et la résolution par pénalisation dualité d’une classe de problèmes de Dirichlet non linéaires, R.A.I.R.O., vol. 2, 1975, p. 41-76. Zbl0368.65053 · Zbl 0368.65053
[8] 8. T. K A T O, Perturbation Theory for Linear Operators, Springer Verlag, Heidelberg-New York, 1966. Zbl0148.12601 MR203473 · Zbl 0148.12601
[9] 9. J. L. LIONS, Quelques méthodes de résolution de problèmes aux limites non linéaires, Dunod, Paris, 1969. Zbl0189.40603 MR259693 · Zbl 0189.40603
[10] 10. M. C. PELISSIER, Sur quelques problèmes non linéaires en glaciologie, Thèse, Université Paris-Sud, 1975. MR439015
[11] 11. P. A. RAVIART et J. M. THOMAS, Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations (à paraître). Zbl0364.65082 · Zbl 0364.65082
[12] 12. P. A. RAVIART et J. M. THOMAS, A Mixed Finite Element Method for 2nd Order Elliptic Problems, (à paraître). Zbl0362.65089 · Zbl 0362.65089
[13] 13. R. TEMAM, Navier Stokes Equations, North Holland, Amsterdam (à paraître en 1976. Zbl0383.35057 MR603444 · Zbl 0383.35057
[14] 14. F. TREVES, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1970. Zbl0171.10402 MR225131 · Zbl 0171.10402
[15] 15. K. YOSIDA, Functional Analysis, Springer Verlag, Heidelberg-New York, 1966. Zbl0435.46002 · Zbl 0435.46002
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