Invariant Foliations for C1Semigroups in Banach Spaces

Journal of Differential Equations

Volumn 139, Issue 2, 1997, Pages 283-318

  Chen, Xu Yan ^a   Hale, Jack K ^a   Tan, Bin ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040652275     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1997.3255     Document Type: Article

References (39)

1. Ball J. M. Saddle point analysis for an ordinary differential equation in a Banach space, and an application to dynamic buckling of a beam. Nonlinear Elasticity. 1973;Academic Press, New York. p. 93-160.
2. Bates P. W., Jones C. K. R. T. Invariant manifolds for semilinear partial differential equations. Dynam. Reported. 2:1988;1-38.
3. Bates P. W., Lu K. A Hartman-Grobman theorem for Cahn-Hilliard equations and phase-field equations. J. Dynam. Differential Equations. 6:1994;101-145.
4. P. W. Bates, K. Lu, C.-C. Zeng, Existence and persistence of invariant manifolds for semiflows in Banach space.
5. Berestycki H., Lions P. L. Nonlinear scalar field equations. II. Existence of infinitely many solutions. Arch. Rational Mech. Anal. 82:1983;347-376.
6. Chafee N. A bifurcation problem for functional differential equations of finitely retarded type. J. Math. Anal. Appl. 35:1971;312-348.
7. Carr J. Application of Center Manifold Theory. Applied Mathematical Sciences. 35:1981;Springer-Verlag, New York.
8. Chen M., Chen X.-Y., Hale J. K. Structural stability for time-periodic one-dimensional parabolic equations. J. Differential Equations. 96:1992;355-418.
9. Chow S.-N., Hale J. K. Methods of Bifurcation Theory. 1982;Springer-Verlag, New York.
10. Chow S.-N., Li C., Wang D. Normal Forms and Bifurcation of Planar Vector Fields. 1994;Cambridge Univ. Press, Cambridge.
11. Chow S.-N., Lin X.-B., Lu K. Smooth invariant foliations in infinite dimensional spaces. J. Differential Equations. 94:1991;266-291.
12. S.-N. Chow, W.-S. Liu, Y. Yi, Center manifolds for invariant manifolds.
13. Chow S.-N., Lu K. Invariant manifolds for flows in Banach spaces. J. Differential Equations. 74:1988;285-317.
14. kcenter unstable manifolds. Proc. Roy. Soc. Edinburgh Sect. A. 108:1988;303-320.
15. Constantin P., Foias C., Nicolaenko B., Temam R. Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations. Applied Mathematical Sciences. 70:1989;Springer-Verlag, Berlin/New York.
16. Da Prato G., Lunardi A. Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space. Arch. Rational Mech. Anal. 101:1988;115-141.
17. Foias C., Sell G., Temam R. Inertial manifolds for nonlinear evolutionary equations. J. Differential Equations. 73:1988;309-353.
18. Hale J. K. Integral manifolds of perturbed differential systems. Ann. Math. 73:1961;486-531.
19. Hale J. K. Asymptotic Behavior of Dissipative Systems. Amer. Math. Soc. 1988.
20. Hale J. K., Lunel S. Introduction to Functional Differential Equations. 1993;Springer-Verlag, Berlin/New York.
21. Hale K., Lin X.-B. Symbolic dynamics and nonlinear flows. Ann. Mat. Pura Appl. 144:1986;229-260.
22. Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics. 840:1981;Springer-Verlag, New York.
23. Hirsch M. W., Pugh C., Shub M. Invariant Manifolds. Lecture Notes in Mathematics. 583:1977;Springer-Verlag, New York.
24. M. C. Irwin, On the stable manifold theorem, Bull. London Math. Soc. 2, 196, 198.
25. Keller C. Stable and unstable manifolds for the nonlinear wave equation with dissipation. J. Differential Equations. 50:1983;330-347.
26. Kelley A. The stable, center-stable, center, center-unstable, unstable manifolds. J. Differential Equations. 3:1967;546-570.
27. Krylov N., Bogoliubov N. N. The Application of Methods of Nonlinear Mechanics to the Theory of Stationary Oscillations. Publication 8, Ukrainian Academy of Science. 1934.
28. J. Kruzweil, 1967, Invariant manifolds for flows, Proc. Sympos. Differential Equations and Dynamical Systems, Academic Press, New York.
29. Kruzweil J. The averaging principle in certain special cases of boundary problems for partial differential equations. Casopis Pěst. Mat. 88:1963;444-456.
30. Lyapunov A. M. Problème géneral de la stabilité du mouvement. Annals of Mathematics Studies. 1949;Princeton Univ. Press.17, Princeton.
31. Mallet-Paret J., Sell G. Inertial manifolds for reaction diffusion equations in higher space dimensions. J. Amer. Math. Soc. 1:1988;805-866.
32. J. Marsden, J. Scheurle, The construction and smoothness of invariant manifolds by deformation method, SIAM J. Math. Anal. 18, 1261, 1274.
33. Pliss V. A. Nonlocal Problems of the Theory of Oscillations. 1966;Academic Press, New York.
34. Robinson J. Inertial manifold and the cone condition. Dynam. Systems Appl. 2:1993;311-330.
35. Sell G., You Y. Inertial manifolds: The non-self adjoint case. J. Differential Equations. 96:1992;203-255.
36. Strauss W. Existence of solitary waves in higher dimensions. Comm. Math. Phys. 55:1977;149-162.
37. A. Vanderbauwhede, S. A. Van Gils, 1987, Center manifolds and contractions on a scale of Banach spaces, 72, 209, 224.
38. Vanderbauwhede A., Iooss G. Center manifold theory in infinite dimensions. Dynam. Reported. 1:1992;125-163.
39. Wells J. C. Invariant manifolds of nonlinear operators. Pacific J. Math. 62:1976;285-293.