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Book Review

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Book Information:

Author: Jack K. Hale
Title: Asymptotic behavior of dissipative systems
Additional book information: Mathematical Surveys and Monographs, vol. 25, American Mathematical Society, Providence, R.I., 1988, ix + 198 pp., $54.00. ISBN 0-8218-1527-x.

References [Enhancements On Off] (What's this?)

  • 1. S. B. Angement, The Morse-Smale property for a semilinear boundary value problem, J. Differential Equations 67 (1987), 212-242.
  • 2. A. V. Babin and M. I. Vishik, Regular attractors of semigroups of evolutionary equations, J. Math. Pures Appl. 62 (1983), 441-491. MR 735932
  • 3. J. E. Billotti and J. P. LaSalle, Periodic dissipative processes, Bull. Amer. Math. Soc. (N. S.) 6 (1971), 1082-1089. MR 284682
  • 4. C. Foias, G. Sell and R. Temam, Inertial manifolds for nonlinear evolution equations, J. Differential Equations 73 (1988), 309-353. MR 943945
  • 5. C. Foias, and R. Temam, Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations, J. Math. Pures Appl. 58 (1979), 339-368. MR 544257
  • 6. J. M. Ghidaglia and J. C. Saut (eds.), Equations aux dérivées partielles non linéaires dissipatives et systèmes dynamiques, Hermann, Paris, 1988. MR 948675
  • 7. J. K. Hale, Asymptotic behavior of dissipative systems, Mathematical Surveys and Monographs n, Amer. Math. Soc., Providence, R. I., 1988. MR 941371
  • 8. J. K. Hale, L. Magalhães and W. Oliva, An introduction to infinite dimensional dynamical systems, Applied Math. Sciences, vol. 47, Springer-Verlag, Berlin and New York, 1984. MR 725501
  • 9. J. K. Hale and G. Raugel, Lower semicontinuity of the attractor for gradient systems, Annali di Mat. Pura e Applicata (1989).
  • 10. D. Henry, Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations, J. Differential Equations 59 (1985), 165-205. MR 804887
  • 11. O. A. Ladyzhenskaya, A dynamical system generated by the Navier-Stokes equatons, Zapiski Nauk. Sem. Leningrad Otd. Math. Instituta Steklova 27 (1972), 91-115. MR 328378
  • 12. O. A. Ladyzhenskaya, Dynamical system generated by the Navier-Stokes equations, Soviet Physics Dokl. 17 (1973), 647-649.
  • 13. N. Levinson, Transformation theory of nonlinear differential equations of the second order, Ann. of Math. (2) 45 (1944), 724-737. MR 11505
  • 14. J. Mallet-Paret, Negatively invariant sets of compact maps and an extension of a theorem of Cartwright, J. Differential Equations 22 (1976), 331-348. MR 423399
  • 15. J. Mallet-Paret and G. Sell, Inertial manifolds for reaction-diffusion equations in higher space dimensions, J. Amer. Math. Soc. 1 (1988), 805-866. MR 943276
  • 16. R. Mañé, On the dimension of the compact invariant sets of certain nonlinear maps, Lecture Notes in Math., vol. 898, Springer-Verlag, Berlin and New York, 1981, pp. 230-242. MR 654892
  • 17. V. Pliss, Nonlocal problems in the theory of oscillations, Academic Press, New York, 1966. MR 196199
  • 18. R. Temam, Infinite dimensional dynamical systems in mechanics and physics, Springer-Verlag, Berlin and New York, 1988. MR 953967

Review Information:

Reviewer: Geneviève Raugel
Journal: Bull. Amer. Math. Soc. 22 (1990), 175-183
DOI: https://doi.org/10.1090/S0273-0979-1990-15875-6
American Mathematical Society