Location of Repository

Lower semicontinuity of attractors for non-autonomous dynamical systems

By Alexandre Nolasco de Carvalho, José A. Langa and James C. Robinson

Abstract

This paper is concerned with the lower semicontinuity of attractors for semilinear\ud non-autonomous differential equations in Banach spaces. We require the unperturbed\ud attractor to be given as the union of unstable manifolds of time-dependent hyperbolic\ud solutions, generalizing previous results valid only for gradient-like systems in which\ud the hyperbolic solutions are equilibria. The tools employed are a study of the continuity\ud of the local unstable manifolds of the hyperbolic solutions and results on the continuity of\ud the exponential dichotomy of the linearization around each of these solutions

Topics: QA
Publisher: Cambridge University Press
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:3137

Suggested articles

Preview

Citations

  1. (2006). A general approximation scheme for attractors of abstract parabolic problems. doi
  2. (1988). Asymptotic Behavior of Dissipative Systems (Mathematical Surveys and doi
  3. (1998). Asymptotic behaviour of non-autonomous difference inclusions. doi
  4. (2002). Attractors for doi
  5. (2005). Bifurcation from zero of a complete trajectory for nonautonomous logistic PDEs. doi
  6. (2008). Continuity of attractors for parabolic problems with localized large diffusion. Nonlinear Anal. doi
  7. (1996). Dynamical Systems and Numerical Analysis. doi
  8. (1999). Existence and persistence of invariant manifolds for semiflows in Banach spaces. doi
  9. (2005). Exponential attractors and finite-dimensional reduction for nonautonomous dynamical systems. doi
  10. (2005). Extremal equilibria and asymptotic behavior of parabolic nonlinearreaction-diffusionequations.NonlinearEllipticandParabolicProblems(ProgressinNonlinear Differential Equations and their
  11. (1981). Geometric Theory of Semilinear Parabolic Equations doi
  12. (1988). Infinite Dimensional Dynamical Systems in Mechanics and doi
  13. (2001). Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. doi
  14. (2007). J.C.RobinsonandA.Suárez.Characterizationofnon-autonomousattractors of a perturbed gradient system.
  15. (1996). Lower semicontinuity of a non-hyperbolic attractor for the viscous CahnHilliard equation. doi
  16. (1995). Lower semicontinuity of a non-hyperbolic attractor. doi
  17. (2004). Lower semicontinuity of attractors for parabolic problems with Dirichlet boundary conditons in varying domains.
  18. (1989). Lower semicontinuity of attractors of gradient systems and applications. doi
  19. (2007). Non-autonomous perturbation of autonomous semilinear differential equations: continuity of local stable and unstable manifolds. doi
  20. (2003). On the upper semicontinuity of cocycle attractors for non-autonomous and random dynamical systems. doi
  21. (2006). Perturbations of foliated bundles and evolutionary equations. doi
  22. (1995). Random attractors. doi
  23. (1999). Robustness of exponential dichotomies in infinite dimensional dynamical systems.
  24. (2004). Spectral convergence and nonlinear dynamics of reaction-diffusion equations under perturbations of the domain. doi
  25. (2002). The relationship between pullback, forward and global attractors of nonautonomous dynamical systems. doi
  26. (2007). The structure of attractors in non-autonomous perturbations of gradient-like systems. doi
  27. (2006). Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations. doi
  28. (2008). Uniformly attracting solutions of nonautonomous differential equations. Nonlinear Anal. doi
  29. (1988). Upper semicontinuity of attractors for approximation of semigroups and partial differential equations. doi
  30. (1998). Upper semicontinuity of attractors for small random perturbations of dynamical systems. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.