Bulletin of the American Mathematical Society

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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.

1.

S. B. Angement, The Morse-Smale property for a semilinear boundary value problem, J. Differential Equations 67 (1987), 212-242.

A. V. Babin and M. I. Vishik, Regular attractors of semigroups and evolution equations, J. Math. Pures Appl. (9) 62 (1983), no. 4, 441–491 (1984). MR 735932

J. E. Billotti and J. P. LaSalle, Dissipative periodic processes, Bull. Amer. Math. Soc. 77 (1971), 1082–1088. MR 284682, DOI 10.1090/S0002-9904-1971-12879-3

Ciprian Foias, George R. Sell, and Roger Temam, Inertial manifolds for nonlinear evolutionary equations, J. Differential Equations 73 (1988), no. 2, 309–353. MR 943945, DOI 10.1016/0022-0396(88)90110-6

C. Foiaş and R. Temam, Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations, J. Math. Pures Appl. (9) 58 (1979), no. 3, 339–368. MR 544257

Jean-Michel Ghidaglia and Jean-Claude Saut, Équations aux dérivées partielles non linéaires dissipatives et systèmes dynamiques, Équations aux dérivées partielles non linéaires dissipatives et systèmes dynamiques, Travaux en Cours, vol. 28, Hermann, Paris, 1988, pp. 11–46 (French). MR 948675

Jack K. Hale, Asymptotic behavior of dissipative systems, Mathematical Surveys and Monographs, vol. 25, American Mathematical Society, Providence, RI, 1988. MR 941371, DOI 10.1090/surv/025

Jack K. Hale, Luis T. Magalhães, and Waldyr M. Oliva, An introduction to infinite-dimensional dynamical systems—geometric theory, Applied Mathematical Sciences, vol. 47, Springer-Verlag, New York, 1984. With an appendix by Krzysztof P. Rybakowski. MR 725501, DOI 10.1007/0-387-22896-9_{9}

9.

J. K. Hale and G. Raugel, Lower semicontinuity of the attractor for gradient systems, Annali di Mat. Pura e Applicata (1989).

Daniel B. Henry, Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations, J. Differential Equations 59 (1985), no. 2, 165–205. MR 804887, DOI 10.1016/0022-0396(85)90153-6

O. A. Ladyženskaja, The dynamical system that is generated by the Navier-Stokes equations, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 27 (1972), 91–115 (Russian). Boundary value problems of mathematical physics and related questions in the theory of functions, 6. MR 0328378

12.

O. A. Ladyzhenskaya, Dynamical system generated by the Navier-Stokes equations, Soviet Physics Dokl. 17 (1973), 647-649.

Norman Levinson, Transformation theory of non-linear differential equations of the second order, Ann. of Math. (2) 45 (1944), 723–737. MR 11505, DOI 10.2307/1969299

John Mallet-Paret, Negatively invariant sets of compact maps and an extension of a theorem of Cartwright, J. Differential Equations 22 (1976), no. 2, 331–348. MR 423399, DOI 10.1016/0022-0396(76)90032-2

John Mallet-Paret and George R. Sell, Inertial manifolds for reaction diffusion equations in higher space dimensions, J. Amer. Math. Soc. 1 (1988), no. 4, 805–866. MR 943276, DOI 10.1090/S0894-0347-1988-0943276-7

Ricardo Mañé, On the dimension of the compact invariant sets of certain nonlinear maps, Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980), Lecture Notes in Math., vol. 898, Springer, Berlin-New York, 1981, pp. 230–242. MR 654892

V. A. Pliss, Nonlocal problems of the theory of oscillations, Academic Press, New York-London, 1966. Translated from the Russian by Scripta Technica, Inc; Translation edited by Harry Herman. MR 0196199

Roger Temam, Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematical Sciences, vol. 68, Springer-Verlag, New York, 1988. MR 953967, DOI 10.1007/978-1-4684-0313-8

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 0735932

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