Continuity of attractors

 Access to full text

 Full (PDF)

1. [1] A. V. BABIN, M. I. VISHIK (1), Regular attractors of semigroupsand evolution quations, J. Math. Pures et Appl. 62, pp. 441-491, 1983. Zbl0565.47045MR735932
2. [2] A. V. BABIN, M. I. VISHIK (2), Unstable invariant sets of semigroups of nonlinear operators and their perturbations, Uspekhi Mat. Nauk 41, pp. 3-34, 1986, Russian Math. Surveys 41, pp. 1-41, 1986. Zbl0624.47065MR863873
3. [3] P. BRUNOVSKY, S.-N. CHOW, Generic properties of stationary solutions of reaction-diffusion equations, J. Diff. Equat. 53, pp. 1-23, 1984. Zbl0544.34019MR747403
4. [4] G. COOPERMAN, α-Condensing maps and dissipative systems, Ph. D. Thesis, Brown Umversity, Providence, R.I., June 1978. 
5. [5] J. M. GHIDAGLIA, R. TEMAM, Attractors for damped nonlinear hyperbolic equations, J. Math. Pures et Appl., 66, pp. 273-319, 1987. Zbl0572.35071MR913856
6. [6] J. K. HALE (1), Asymptotic behavior and dynamics in infinite dimensions, in Nonlinear Differential Equations, J. K. Hale and P. Martinez-Amores, Eds., Pittman 132, 1985. Zbl0653.35006
7. [7] J. K. HALE (2), Asymptotic Behavior of Dissipative Systems, Surveys and Monographs, Vol. 25, A.M.S., Providence, R.I., 1988. Zbl0642.58013MR941371
8. [8] J. K. HALE, X. B. LIN, G. RAUGEL, Upper-semicontinuity of attractors for approximations of semigroups and partial differential equations, Math. of Comp., 50, pp. 89-123, 1988. Zbl0666.35013MR917820
9. [9] J. K. HALE, L. MAGALHAES, W. OLIVA, An Introduction to Infinite Dimensional Dynamical Systems, Applied Math. Sciences, Vol. 47, Springer Verlag, 1984. Zbl0533.58001MR725501
10. [10] J. K. HALE, G. RAUGEL (1), Upper-semicontinuity of the attractor for a singularly perturbed hyperbolic equation, J. Diff. Equat., 73, pp. 197-214, 1988. Zbl0666.35012MR943939
11. [11] J. K. HALE, G. RAUGEL (2), Lower-semicontinuity of attractors of gradient systems and applications, Ann. Mat. Pura e App., to appear. Zbl0712.47053MR1043076
12. [12] J. K. HALE, G. RAUGEL (3), Lower-semicontinuity of the singularly perturbed hyperbolic equation, DDE., to appear. Zbl0752.35034
13. [13] J. K. HALE, G. RAUGEL (4), A reaction-diffusion equation on a thin domain, preprint. Zbl0828.35055
14. [14] J. K. HALE, G. RAUGEL (5), Morse-Smale property for a singularly perturbed hyperbolic equation, in preparation. Zbl0666.35012
15. [15] J. K. HALE, C. ROCHA, Interaction of diffusion and boundary conditions, Nonlinear Analysis, T.M.A., 11, pp. 633-649, 1987. Zbl0661.35047MR886654
16. [16] A. HARAUX, Two remarks on dissipative hyperbolic problems, Séminaire du Collège de France, J. L. Lions Ed., Pittman, Boston, 1985. Zbl0579.35057
17. [17] D. HENRY (1), Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math, Vol. 840, Springer Verlag, 1981. Zbl0456.35001MR610244
18. [18] D. HENRY (2), Some infinite-dimensional Morse-Smale Systems defined by parabolic partial differential equations, J. Diff. Equat. 59, pp. 165-205, 1985. Zbl0572.58012MR804887
19. [19] D. HENRY (3), Generic properties of equilibrium solutions by perturbation of the boundary, Preprint of the « Centre de Recerca Matematica Institut d'Estudis Catalans», 37, 1986. Zbl0656.35069MR921906
20. [20] X. MORÀ, J. SOLA-MORALES, The singular limit dynamics of semilinear damped wave equations, J. Diff. Equat., to appear. Zbl0699.35177MR992148
21. [21] J. PALIS, W. DE MELO, Geometric Theory of Dynamical Systems, Springer Verlag, 1982. Zbl0491.58001MR669541
22. [22] C. ROCHA, Generic properties of equilibria of reaction-diffusion equations with variable diffusion, Proc. Roy. Soc. Edinburgh, 101A, pp. 45-56, 1985. Zbl0601.35053MR824206
23. [23] J. SMOLLER, A. WASSERMANGeneric bifurcation of steady-state solutions, J.Diff. Equat. 52, pp. 432-438, 1984. Zbl0488.58015MR744306