Contingent solutions to the center manifold equation

Jean-Pierre Aubin; Guiseppe Da Prato

Annales de l'I.H.P. Analyse non linéaire (1992)

  • Volume: 9, Issue: 1, page 13-28
  • ISSN: 0294-1449

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Aubin, Jean-Pierre, and Da Prato, Guiseppe. "Contingent solutions to the center manifold equation." Annales de l'I.H.P. Analyse non linéaire 9.1 (1992): 13-28. <http://eudml.org/doc/78269>.

@article{Aubin1992,
author = {Aubin, Jean-Pierre, Da Prato, Guiseppe},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {ordinary differential equations; center manifold; partial differential inclusions; contingent derivative; global bounded and Lipschitzian contingent solution; viscosity method},
language = {eng},
number = {1},
pages = {13-28},
publisher = {Gauthier-Villars},
title = {Contingent solutions to the center manifold equation},
url = {http://eudml.org/doc/78269},
volume = {9},
year = {1992},
}

TY - JOUR
AU - Aubin, Jean-Pierre
AU - Da Prato, Guiseppe
TI - Contingent solutions to the center manifold equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 1
SP - 13
EP - 28
LA - eng
KW - ordinary differential equations; center manifold; partial differential inclusions; contingent derivative; global bounded and Lipschitzian contingent solution; viscosity method
UR - http://eudml.org/doc/78269
ER -

References

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  3. [3] J.-P. Aubin and H. Frankowska, Set-ValuedAnalysis, Birkhäuser, Boston, Basel, 1990. Zbl0713.49021MR1048347
  4. [4] J.-P. Aubin and H. Frankowska, Contingent partial Differential Equations Governing Feedback Controls, Preprint (to appear). Zbl0840.93041MR1446213
  5. [5] J.-P. Aubin, Viability Theory, Birkhäuser, Boston, Basel, 1991. Zbl0755.93003MR1134779
  6. [6] C.I. Byrnes and A. Isidori, A Frequency Domain Philosophy for Nonlinear Systems, with applications to stabilization and adaptive control, 23rd I.E.E.E. Conf. Dec. Control, 1984, pp. 1569-1573 in Comutation and Control, K. BOWERS and J. LUND Eds., Birkhäuser, pp. 23-52. 
  7. [7] C.I. Byrnes and A. Isidori, Output Regulation of Non linear Systems, I.E.E.E. Trans. Automn. Control, Vol. 35, 1990, pp. 131-140. Zbl0704.93034MR1038409
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  9. [9] I. Capuzzo Dolcetta and J.L. Menaldi, Asymptotic Behavior of the First Order Obstacle Problem, J. Diff. Eq., Vol. 75, 1988, pp. 303-328. Zbl0674.35011MR961158
  10. [10] P. Cannarsa and G. Da Prato, Direct Solutions of a Second-Order Hamilton-Jacobi Equation in Hilbert Spaces, Preprint (to appear). Zbl0805.49016MR1222689
  11. [11] J. Carr, Applications of Centre Manifold Theory, Springer-Verlag, 1981. Zbl0464.58001MR635782
  12. [12] G. Da Prato and A. Lunardi, Stability, Instability and Center Manifold Theorem for Fully Nonlinear Autonomous Parabolic Equations in Banach Spaces, Arch. Rat. Mech. Anal., Vol. 101, 1988, pp. 115-141. Zbl0661.35044MR921935
  13. [13] L.C. Evans and P.E. Souganidis, Fully Nonlinear Second Order Elliptic Equations With Large Order Coefficient, Ann. Inst. Fourier, Vol. 31, 1981, pp. 175-191. Zbl0441.35023MR617246
  14. [14] H. Frankowska, L'équation d'Hamilton-Jacobi contingente, C.R. Acad. Sci. Paris, T. 304, Series I, 1987, pp. 295-298. Zbl0612.49023MR886727
  15. [15] H. Frankowska, Optimal trajectories associated a solution of Hamilton-Jacobi Equations, I.E.E.E., 26th, CDC Conference, Los Angeles, December 9-11, 1987. 
  16. [16] H. Frankowska, Nonsmooth solutions of Hamilton-Jacobi-Bellman Equations, Proceedings of the International Conference Bellmann Continuum, Antibes, France, June 13- 14, 1988, Lecture Notes in Control and Information Sciences, Springer Verlag. Zbl0762.49011MR1231118
  17. [17] O. Hijab, Discounted Control of Degenerate Diffusions in Rd, preprint (to appear). 
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  19. [19] A. Lunardi, Existence in the small and in the large in Fully Nonlinear Parabolic Equations, in Differencia Equations and Applications, Ed. Aftabizadeh, Ohio University Press, 1988. Zbl0727.35072MR1026215

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