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Global attractors and regularity for the extensible suspension bridge equations with past history

Qiaozhen Ma|Shifang Liu
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2016.09|한국수학논문집 (Korean Journal of Mathematics)|제24권 제3호|pp. 375-395|DOI http://dx.doi.org/10.11568/kjm.2016.24.3.375

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참고문헌

키워드

past historyextensible suspension bridge equationsglobal attractorsa bounded absorbing set
주제분류수학

초록

In this paper, we study the long-time dynamical behavior for the extensible suspension bridge equations with past history. We prove the existence of the global attractors by using the contraction function method. Furthermore, the regularity of global attractor is achieved.

Abstract

In this paper, we study the long-time dynamical behavior for the extensible suspension bridge equations with past history. We prove the existence of the global attractors by using the contraction function method. Furthermore, the regularity of global attractor is achieved.

참고문헌 (19)

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  4. J.R. Kang, "Pullback attractors for the non-autonomous coupled suspension bridge equations", Appl. Math. Comput, 219, pp.8747~8758 (2013)
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  7. Q.Z. Ma, "uniform compact attractors for the coupled suspension bridge equations", Appl. Math. Comput, 15, pp.6604~6615 (2011)
  8. J.Y. Park, "Pullback D-attractors for non-autonomous suspension bridge equations", Nonlinear Anal, 71, pp.4618~4623 (2009)
  9. J.Y. Park, "Global attractor for suspension bridge equation with nonlinear damping", Quart. Appl. Math, 69, pp.465~475 (2011)
  10. L. Xu, "Existence of random attractors for the floating beam equation with strong damping and white noise", Boundry Value Problem, 126, pp.1~13 (2015)
  11. J.M. Ball, "Initial-boundary value problems for an extensible beam", J. Math. Anal. Appl, 42, pp.61~90 (1973)
  12. J.M. Ball, "Stability theory for an extensible beam", J. Diff. Equ, 14, pp.399~418 (1973)
  13. I. Bochicchio, "Long-term damped dynamics of the extensible suspension bridge", Int. J. Diff. Equ, 10, pp.1155~1174 (2010)
  14. Q.Z. Ma, "Random attractors for the extensible suspension bridge equation with white noise", Comput. Math. Appl, 70, pp.2895~2903 (2015)
  15. J.R. Kang, "Long-time behavior of a suspension bridge equations with past history", Appl. Math. Comput, 265, pp.509~519 (2015)
  16. M. Fabrizio, "A new approach to equations with memory", Arch. Ration, Mech. Anal, 198, pp.189~232 (2010)
  17. V. Pata, "Attractors for a damped hyperbolic equation with linear memory", Math. Sci. Appl, 2, pp.505~529 (2001)
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  19. R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics" (1988), Springer-Verlag

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