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GLOBAL ATTRACTOR FOR SOME BEAM EQUATION WITH NONLINEAR SOURCE AND DAMPING TERMS

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영남수학회 (Youngnam Mathematical Society)|2016.05|East Asian Mathematical Journal|제32권 제3호|pp. 377-385|DOI http://dx.doi.org/10.7858/eamj.2016.028

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참고문헌

키워드

Beam equationGlobal attractorLong-time behavior
주제분류수학

초록

Global attractor is a basic concept to study the long-time behavior of solutions of the various equations. This paper is investigated with the existence of a global attractor for the beam equation utt+△2u-▽‧{σ|▽u|2)▽u}+f(u)+a(x)g(ut)=h, using multipliers technique and Nakao's Lemma.

Abstract

Global attractor is a basic concept to study the long-time behavior of solutions of the various equations. This paper is investigated with the existence of a global attractor for the beam equation utt+△2u-▽‧{σ|▽u|2)▽u}+f(u)+a(x)g(ut)=h, using multipliers technique and Nakao's Lemma.

참고문헌 (19)

  1. J. M. Ball, "Stability theory for an extensible beam", J. Differential Equations, 14, pp.399~418 (1973)
  2. J. M. Ball, "Initial-boundary value problems for an extensible beam", J. Math. Anal. Appl., 42, pp.61~90 (1973)
  3. A. V. Babin, "Attrators of evolution equations" (1992), North-Holland
  4. R. W. Dickey, "Free vibrations and dynamic buckling of the extensible beam", J. Math. Anal. Appl., 29, pp.443~454 (1970)
  5. R. W. Dickey, "Dynamic stability of equilibrium states of the extensible beam", J. Proc. Amer. Math. Soc., 41, pp.94~102 (1973)
  6. C. M. Dafermos, "Asymptotic behavior of solutions of evolution equations in nonlinear evolution equations", Funkcial. Ekvac., 38, pp.545~568 (1995)
  7. J. K. Hale, "Asymptotic behavior of dissipative systems" (1988), AMS
  8. A. Kh. Khanmamedov, "Existence of a global attractor for the plate equation with the critical exponent in an unbounded domain", Appl. Math. Letter, 18, pp.827~832 (2005)
  9. A. Kh. Khanmamedov, "Global attractors for plate equation with a localized damping and critical exponent in an unbounded domain", J. Differential Equations, 225, pp.528~548 (2006)
  10. To Fu Ma, "Global attractor for a model of extensible beam with nonlinear damping and source terms", Nonlinear Anal., 73, pp.3402~3412 (2010)
  11. M. Nakao, "Global attractors for wave equaitons with nonlinear dissipative terms", J. Differential Equations, 227, pp.204~229 (2006)
  12. M. Nakao, "Global attractors for some quasi-linear wave equations with a strong with a strong dissipation", Advances in Math. Sciences Appl., 17(1), pp.89~105 (2007)
  13. M. Nakao, "On global attractors for a nonlinear parabolic equation of m-laplacian type in RN", Funkcialaj Ekvacioj, 50, pp.449~458 (2007)
  14. M. Nakao, "On global attractor for nonlinear parabolic equations of m-laplacian type", J. Math. Anal. Appl., 331, pp.793~809 (2007)
  15. R. Temam, "Infinite dimensional dynamic system in meachanics and physics" (1997), Springer
  16. Y. Xie, "Asymptotic behavior of a class of nonlinear evolution equations", Non-linear Anal., 71, pp.5095~5105 (2009)
  17. L. Yang, "Global attractor for plate equation with nonlinear damping", Nonlinear Anal., 69, pp.3802~3810 (2008)
  18. G. Yue, "Golbal attractors for plate equations with critical exponent in locallay uniform spaces", Nonlinear Anal., 71, pp.4105~4114 (2009)
  19. Y. Zhijian, "Longtime behavior for a nonlinear wave equation arising in elasto-plastic flow", Math. Meth. Appl. Sci., 32, pp.1082~1104 (2009)

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