References: |
[1] E. A. M. Abreu and A. N. Carvalho. Lower semicontinuity of attractors for parabolic problems with Dirichlet boundary conditons in varying domains. Mat. Contemp. 27 (2004), 37–51. [2] J. M. Arrieta and A. N. Carvalho. Spectral convergence and nonlinear dynamics of reaction-diffusion equations under perturbations of the domain. J. Differential Equations 199 (2004), 143–178. [3] P. Bates, K. Lu and C. Zeng. Existence and persistence of invariant manifolds for semiflows in Banach spaces. Mem. Amer. Math. Soc. 135(645) (1999). [4] A. Berger and S. Siegmund. Uniformly attracting solutions of nonautonomous differential equations. Nonlinear Anal. 68(12) (2008), 3789–3811. [5] S. M. Bruschi, A. N. Carvalho, J. W. Cholewa and T. Dłotko. Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations. J. Dynam. Differential Equations 18 (2006), 767–814. [6] T. Caraballo, J. A. Langa and J. C. Robinson. Upper semicontinuity of attractors for small random perturbations of dynamical systems. Comm. Partial Differential Equations 23(9–10) (1998), 1557–1581. [7] T. Caraballo and J. A. Langa. On the upper semicontinuity of cocycle attractors for non-autonomous and random dynamical systems. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 10(4) (2003), 491–513. [8] V. L. Carbone, A. N. Carvalho and K. Schiabel-Silva. Continuity of attractors for parabolic problems with localized large diffusion. Nonlinear Anal. 68(3) (2008), 515–535. [9] A. N. Carvalho and S. Piskarev. A general approximation scheme for attractors of abstract parabolic problems. Numer. Funct. Anal. Optim. 27 (2006), 785–829. [10] A. N. Carvalho and J. A. Langa. Non-autonomous perturbation of autonomous semilinear differential equations: continuity of local stable and unstable manifolds. J. Differential Equations 233(2) (2007), 622–653. [11] A. N. Carvalho, J. A. Langa, J. C. Robinson and A. Suárez. Characterization of non-autonomous attractors of a perturbed gradient system. J. Differential Equations 236 (2007), 570–603. [12] H. Crauel, A. Debussche and F. Flandoli. Random attractors. J. Dynam. Differential Equations 9 (1995), 307–341. [13] D. N. Cheban, P. E. Kloeden and B. Schmalfuß. The relationship between pullback, forward and global attractors of nonautonomous dynamical systems. Nonlinear Dyn. Syst. Theory 2(2) (2002), 125–144. [14] V. V. Chepyzhov and M. I. Vishik. Attractors for Equations of Mathematical Physics (AMS Colloquium Publications, 49). American Mathematical Society, Providence, RI, 2002. [15] M. Efendiev, S. Zelik and A. Miranville. Exponential attractors and finite-dimensional reduction for nonautonomous dynamical systems. Proc. Roy. Soc. Edinburgh Sect. A 135(4) (2005), 703–730. [16] C. M. Elliott and I. N. Kostin. Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn- Hilliard equation. Nonlinearity 9 (1996), 687–702. [17] J. K. Hale, X. B. Lin and G. Raugel. Upper semicontinuity of attractors for approximation of semigroups and partial differential equations. J. Math. Comput. 50 (1988), 89–123. [18] J. K. Hale. Asymptotic Behavior of Dissipative Systems (Mathematical Surveys and Monographs, 25). American Mathematical Society, Providence, RI, 1988. [19] J. K. Hale and G. Raugel. Lower semicontinuity of attractors of gradient systems and applications. Ann. Mat. Pura Appl. 154(4) (1989), 281–326. [20] D. Henry. Geometric Theory of Semilinear Parabolic Equations (Lecture Notes in Mathematics, 840). Springer, Berlin, 1981. [21] P. E. Kloeden and B. Schmalfuß. Asymptotic behaviour of non-autonomous difference inclusions. Systems Control Lett. 33 (1998), 275–280. [22] I. N. Kostin. Lower semicontinuity of a non-hyperbolic attractor. J. London Math. Soc. 52 (1995), 568–582. [23] J. A. Langa, J. C. Robinson, A. Suárez and A. Vidal-López. The structure of attractors in non-autonomous perturbations of gradient-like systems. J. Differential Equations 234(2) (2007), 607–625. [24] J. A. Langa, J. C. Robinson and A. Suárez. Bifurcation from zero of a complete trajectory for nonautonomous logistic PDEs. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 15(8) (2005), 2663–2669. [25] V. A. Pliss and G. R. Sell. Robustness of exponential dichotomies in infinite dimensional dynamical systems. J. Dynam. Differential Equations 11 (1999), 471–513. [26] V. A. Pliss and G. R. Sell. Perturbations of foliated bundles and evolutionary equations. Ann. Mat. Pura Appl. (4) 185(Suppl.) (2006), S325–S388. [27] J. C. Robinson. Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. Cambridge University Press, Cambridge, 2001. [28] A. Rodríguez-Bernal and A. Vidal-López. Extremal equilibria and asymptotic behavior of parabolic nonlinear reaction-diffusion equations. Nonlinear Elliptic and Parabolic Problems (Progress in Nonlinear Differential Equations and their Applications, 64). Birkhäuser, Basel, 2005, pp. 509–516. [29] A. M. Stuart and A. R. Humphries. Dynamical Systems and Numerical Analysis. Cambridge University Press, Cambridge, 1996. [30] R. Temam. Infinite Dimensional Dynamical Systems in Mechanics and Physics. Springer, New York, 1988. |