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The Global and Pullback Attractors for a Strongly Damped Wave Equation with Delays*
Department of Mathematics, Yunnan University, Kunming, China
Department of Mathematics, Yunnan University, Kunming, China
School of Mathematics and Science, Kaili University, Kaili, China
- 1 Department of Mathematics, Yunnan University, Kunming, China
- 2 Department of Mathematics, Yunnan University, Kunming, China
- 3 School of Mathematics and Science, Kaili University, Kaili, China
International Journal of Modern Nonlinear Theory and Application·Volume 02 (2013)·Pages 209–218·Published 29 November 2013·DOI10.4236/ijmnta.2013.24029
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Abstract
In this paper, w e study the global and pullback attractors for a strongly damped wave equation with delays when the force term belongs to different space. The results follow ing from the solution generate a compact set.
KeywordsStrongly DampedPullback AttractorGlobal AttractorDelays
- J. C. Robinson, “Infinite Dimensional Dynamical Systems,” Cambridge University Press, London, 2001. http://dx.doi.org/10.1007/978-94-010-0732-0
- R. Temam, “Infinite Dimensional Dynamical Systems in Mechanics and Physics,” Springer-Verlag, New York, 1988. http://dx.doi.org/10.1007/978-1-4684-0313-8
- C. K. Zhong, M. H. Yang and C. Y. Sun, “The Existence of Global Attractors for the Norm-to-Weak Continuous Semigroup,” Journal of Differential Equations, Vol. 223, No. 2, 2006, pp. 367-399.
- Y. Q. Xie and C. k. Zhong, “The Existence of Global Attractor for a Class of Nonlinear Evolution Equation,” Journal of Applied Analysis, Vol. 336, No. 1, 2007, pp. 54-69. http://dx.doi.org/10.1016/j.jmaa.2006.03.086
- T. Caraballo, P. E. Kloeden and J. Real, “Pullback and Forward Attractor for a Damped Wave Equation with Delays,” Stochastics and Dynamics, Vol. 4, No. 3, 2004, pp. 405-423. http://dx.doi.org/10.1142/S0219493704001139
- V. Pata and M. Squassina, “On the Strongly Damped Wave Equation,” Communications in Mathematical Physics, Vol. 253, No. 3, 2005, pp. 511-533. http://dx.doi.org/10.1007/s00220-004-1233-1
- T. Caraballo and J. A. Langa, “On the Upper Semicontinuity of Cocycle Attractors for Non-Autonomous and Random Dynamical Systems,” Dynamics of Continuous Discrete and Impulsive Systems, Vol. 10, 2003, pp. 491-513.
- T. Caraballo, P. Marin-Rubio and J. Valero, “Autonomous and Non-Autonomous Attractors for Differential Equations with Delays,” Journal of Differential Equations, Vol. 208, No. 1, 2005, pp. 9-41.
- T. Caraballo and J. Real, “Attractors for 2D-Navier-Stokes Models with Delays,” Journal of Differential Equations, Vol. 205, No. 2, 2004, pp. 270-296. http://dx.doi.org/10.1016/j.jde.2004.04.012
- D. Cheban, P. E. Kloeden and B. Schmalfuss, “The Relationship between Pullback, Forwards and Global Attractors of Nonautonomous Dynamical Systems,” Nonlinear Dynamics and Systems Theory, Vol. 2, 2002, pp. 9-28.
- C. Y. Sun, S. h. Wang and C. K. Zhong, “Global Attractors for a Nonlassical Diffusion Equation,” Acta Mathematica Sinica, English Series, Vol. 26B, No. 3, 2005, pp. 1-8.
- J. Hale, “Asymptotic Behavior of Dissipative Systems,” American Mathematical Society, Providence, 1988.
- M. J. Garrido-Atienza and J. Real, “Existence and Uniqueness of Solutions for Delay Evolution Equations of Second Order in Time,” Journal of Mathematical Analysis and Applications, Vol. 283, No. 2, 2003, pp. 582-609.