• Previous Article
    Error in approximation of Lyapunov exponents on inertial manifolds: The Kuramoto-Sivashinsky equation
  • DCDS-B Home
  • This Issue
  • Next Article
    Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions
May  2008, 9(3&4, May): 581-593. doi: 10.3934/dcdsb.2008.9.581

Equi-Attraction and the continuous dependence of attractors on time delays

1. 

FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.

2. 

Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080–Sevilla, Spain

Received  September 2006 Revised  January 2007 Published  February 2008

Under appropriate regularity conditions it is shown that the continuous dependence of the global attractors $\mathcal{A}_\tau$ of semi dynamical systems $S^{(\tau)}(t)$ in $C([-\tau,0];Z)$ with $Z$ a Banach space and time delay $\tau \in [T_*,T^$*$]$, where $T_* > 0$, is equivalent to the equi-attraction of the attractors. Examples and counter examples posed in this right framework are provided.
Citation: P.E. Kloeden, Pedro Marín-Rubio. Equi-Attraction and the continuous dependence of attractors on time delays. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 581-593. doi: 10.3934/dcdsb.2008.9.581
[1]

Tomás Caraballo, Alexandre N. Carvalho, Henrique B. da Costa, José A. Langa. Equi-attraction and continuity of attractors for skew-product semiflows. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 2949-2967. doi: 10.3934/dcdsb.2016081

[2]

Michael Dellnitz, Mirko Hessel-Von Molo, Adrian Ziessler. On the computation of attractors for delay differential equations. Journal of Computational Dynamics, 2016, 3 (1) : 93-112. doi: 10.3934/jcd.2016005

[3]

Piotr Kalita, Grzegorz Łukaszewicz, Jakub Siemianowski. On relation between attractors for single and multivalued semiflows for a certain class of PDEs. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1199-1227. doi: 10.3934/dcdsb.2019012

[4]

Ting Li. Pullback attractors for asymptotically upper semicompact non-autonomous multi-valued semiflows. Communications on Pure & Applied Analysis, 2007, 6 (1) : 279-285. doi: 10.3934/cpaa.2007.6.279

[5]

Tomás Caraballo, Francisco Morillas, José Valero. On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 51-77. doi: 10.3934/dcds.2014.34.51

[6]

Sylvia Novo, Carmen Núñez, Rafael Obaya, Ana M. Sanz. Skew-product semiflows for non-autonomous partial functional differential equations with delay. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4291-4321. doi: 10.3934/dcds.2014.34.4291

[7]

Julia García-Luengo, Pedro Marín-Rubio, José Real. Regularity of pullback attractors and attraction in $H^1$ in arbitrarily large finite intervals for 2D Navier-Stokes equations with infinite delay. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 181-201. doi: 10.3934/dcds.2014.34.181

[8]

Tomás Caraballo, P.E. Kloeden, Pedro Marín-Rubio. Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay. Discrete & Continuous Dynamical Systems - A, 2007, 19 (1) : 177-196. doi: 10.3934/dcds.2007.19.177

[9]

Fuke Wu, Peter E. Kloeden. Mean-square random attractors of stochastic delay differential equations with random delay. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1715-1734. doi: 10.3934/dcdsb.2013.18.1715

[10]

Antônio Luiz Pereira, Severino Horácio da Silva. Continuity of global attractors for a class of non local evolution equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 1073-1100. doi: 10.3934/dcds.2010.26.1073

[11]

Bernd Aulbach, Martin Rasmussen, Stefan Siegmund. Invariant manifolds as pullback attractors of nonautonomous differential equations. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 579-596. doi: 10.3934/dcds.2006.15.579

[12]

Tomás Caraballo, Gábor Kiss. Attractors for differential equations with multiple variable delays. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1365-1374. doi: 10.3934/dcds.2013.33.1365

[13]

Hammamia Mohamed Ali, Lassaad Mchiria, Sana Netchaoui, Stefanie Sonner. Pullback exponential attractors for differential equations with variable delays. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-19. doi: 10.3934/dcdsb.2019183

[14]

Hongyong Cui, Mirelson M. Freitas, José A. Langa. On random cocycle attractors with autonomous attraction universes. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3379-3407. doi: 10.3934/dcdsb.2017142

[15]

Tomás Caraballo, P.E. Kloeden. Non-autonomous attractors for integro-differential evolution equations. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 17-36. doi: 10.3934/dcdss.2009.2.17

[16]

Francisco Balibrea, José Valero. On dimension of attractors of differential inclusions and reaction-diffussion equations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 515-528. doi: 10.3934/dcds.1999.5.515

[17]

Tomás Caraballo, M. J. Garrido-Atienza, B. Schmalfuss, José Valero. Non--autonomous and random attractors for delay random semilinear equations without uniqueness. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 415-443. doi: 10.3934/dcds.2008.21.415

[18]

Igor Chueshov, Alexander V. Rezounenko. Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1685-1704. doi: 10.3934/cpaa.2015.14.1685

[19]

John M. Ball. Global attractors for damped semilinear wave equations. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 31-52. doi: 10.3934/dcds.2004.10.31

[20]

Ioana Moise, Ricardo Rosa, Xiaoming Wang. Attractors for noncompact nonautonomous systems via energy equations. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 473-496. doi: 10.3934/dcds.2004.10.473

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]