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GLOBAL ATTRACTOR FOR SOME BEAM EQUATION WITH NONLINEAR SOURCE AND DAMPING TERMS
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 Title & Authors
GLOBAL ATTRACTOR FOR SOME BEAM EQUATION WITH NONLINEAR SOURCE AND DAMPING TERMS
Lee, Mi Jin;
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 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 $$u_{tt}+{\Delta}^2u-{\nabla}{\cdot}\{{\sigma}({\mid}{\nabla}u{\mid}^2){\nabla}u\}+f(u)+a(x)g(u_t)
 Keywords
Beam equation;Global attractor;Long-time behavior;
 Language
English
 Cited by
 References
1.
J. M. Ball, Stability theory for an extensible beam, J. Differential Equations 14 (1973),399-418. crossref(new window)

2.
J. M. Ball, Initial-boundary value problems for an extensible beam, J. Math. Anal. Appl. 42 (1973), 61-90. crossref(new window)

3.
A. V. Babin, M. I. Vishik, Attrators of evolution equations, Nauka, Moscow, 1989(1992) (English translation, North-Holland 1992).

4.
R. W. Dickey, Free vibrations and dynamic buckling of the extensible beam, J. Math. Anal. Appl. 29 (1970) 443-454. crossref(new window)

5.
R. W. Dickey, Dynamic stability of equilibrium states of the extensible beam, J. Proc. Amer. Math. Soc. 41 (1973) 94-102. crossref(new window)

6.
C. M. Dafermos, Asymptotic behavior of solutions of evolution equations in nonlinear evolution equations(M. G. Crandall, ed.), Funkcial. Ekvac. 38 (1995) 545-568.

7.
J. K. Hale, Asymptotic behavior of dissipative systems, AMS, Providence, RI, 1988.

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 (2005) 827-832. crossref(new window)

9.
A. Kh. Khanmamedov, Global attractors for plate equation with a localized damping and critical exponent in an unbounded domain, J. Differential Equations 225 (2006) 528-548. crossref(new window)

10.
To Fu Ma, V. Narciso, Global attractor for a model of extensible beam with nonlinear damping and source terms, Nonlinear Anal. 73 (2010) 3402-3412. crossref(new window)

11.
M. Nakao, Global attractors for wave equaitons with nonlinear dissipative terms, J. Differential Equations 227 (2006) 204-229. crossref(new window)

12.
M. Nakao, Global attractors for some quasi-linear wave equations with a strong with a strong dissipation, Advances in Math. Sciences Appl. 17 (2007), no.1, 89-105.

13.
M. Nakao and C. Chen, On global attractors for a nonlinear parabolic equation of m-laplacian type in RN, Funkcialaj Ekvacioj 50 (2007) 449-458. crossref(new window)

14.
M. Nakao and N. Aris, On global attractor for nonlinear parabolic equations of m-laplacian type, J. Math. Anal. Appl. 331 (2007) 793-809. crossref(new window)

15.
R. Temam, Infinite dimensional dynamic system in meachanics and physics, Springer, New York, 1997.

16.
Y. Xie, C. Zhong, Asymptotic behavior of a class of nonlinear evolution equations, Nonlinear Anal. 71 (2009) 5095-5105. crossref(new window)

17.
L. Yang, C. Zhong, Global attractor for plate equation with nonlinear damping, Nonlinear Anal. 69 (2008) 3802-3810. crossref(new window)

18.
G. Yue, C. Zhong, Golbal attractors for plate equations with critical exponent in locallay uniform spaces, Nonlinear Anal. 71 (2009) 4105-4114. crossref(new window)

19.
Y. Zhijian, Longtime behavior for a nonlinear wave equation arising in elasto-plastic flow, Math. Meth. Appl. Sci. 32 (2009) 1082-1104. crossref(new window)