The stability of attractors for non-autonomous perturbations of gradient-like systems

Journal of Differential Equations

Volumn 234, Issue 2, 2007, Pages 607-625

  Langa, José A ^a   Robinson, James C ^b   Suárez, Antonio ^a   Vidal López, Alejandro ^c  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846279832     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2006.11.016     Document Type: Article

References (18)

1. Ball J.M., and Peletier L.A. Global attraction for the one-dimensional heat equation with nonlinear time-dependent boundary conditions. Arch. Ration. Mech. Anal. 65 (1977) 193-201
2. Caraballo T., and Langa J.A. On the upper semicontinuity of cocycle attractors for non-autonomous and random dynamical systems. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 10 (2003) 491-513
3. Carvalho A.N., and Langa J.A. The existence and continuity of stable and unstable manifolds for semilinear problems under non-autonomous perturbation in Banach spaces. J. Differential Equations 233 (2007) 622-653
4. A.N. Carvalho, J.A. Langa, J.C. Robinson, A. Suárez, Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system, preprint, 2006
5. Cheban D.N. Global Attractors of Non-Autonomous Dissipative Dynamical Systems (2004), World Scientific, New Jersey
6. Chepyzhov V.V., and Vishik M.I. Attractors for Equations of Mathematical Physics. Amer. Math. Soc. Colloq. Publ. vol. 49 (2002), Amer. Math. Soc., Providence, RI
7. Crauel H., Debussche A., and Flandoli F. Random attractors. J. Dynam. Differential Equations 9 (1997) 307-341
8. Hale J.K. Asymptotic Behavior of Dissipative Systems. Math. Surveys Monogr. vol. 25 (1988), Amer. Math. Soc., Providence, RI
9. Hale J.K., LaSalle J.P., and Slemrod M. Theory of a general class of dissipative processes. J. Math. Anal. Appl. 39 (1972) 177-191
10. Hale J.K., Magalhaes L.T., and Oliva W. Dynamics in Infinite Dimension (2002), Springer-Verlag, New York
11. Hale J.K., and Raugel G. Lower semicontinuity of attractors of gradient systems and applications. Ann. Mat. Pura Appl. 154 (1989) 281-326
12. Kloeden P.E., and Schmalfuß B. Asymptotic behaviour of non-autonomous difference inclusions. Systems Control Lett. 33 (1998) 275-280
13. Ladyzhenskaya O.A. Attractors for Semigroups and Evolution Equations (1991), Cambridge Univ. Press, Cambridge
14. Langa J.A., Robinson J.C., and Suárez A. Stability, instability, and bifurcation phenomena in non-autonomous differential equations. Nonlinearity 15 (2002) 887-903
15. Robinson J.C. Infinite-Dimensional Dynamical Systems (2001), Cambridge Univ. Press, Cambridge
16. Schmalfuß B. Attractors for the non-autonomous dynamical systems. International Conference on Differential Equations, vols. 1, 2. Berlin, 1999 (2000), World Scientific, River Edge, NJ 684-689
17. Stuart A.M., and Humphries A.R. Dynamical Systems and Numerical Analysis (1996), Cambridge Univ. Press, Cambridge
18. Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics (1988), Springer-Verlag, Berlin