The paper studies the existence of the finite-dimensional global attractor and exponential attractor for the dynamical system associated with the Kirchhoff models arising in elasto-plastic flow . By using the method of -trajectories and the operator technique, it proves that under subcritical case, , the above-mentioned dynamical system possesses in different phase spaces a finite-dimensional (weak) global attractor and a weak exponential attractor, respectively. For application, the fact shows that for the concerned elasto-plastic flow the permanent regime (global attractor) can be observed when the excitation starts from any bounded set in phase space, and the fractal dimension of the attractor, that is, the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow, is finite.
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September 2010
Research Article|
September 10 2010
Finite-dimensional attractors for the Kirchhoff models
Yang Zhijian
Yang Zhijian
a)
Department of Mathematics,
Zhengzhou University
, No.75 Daxue Road, Zhengzhou 450052, People’s Republic of China
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a)
Electronic mail: yzjzzut@tom.com.
J. Math. Phys. 51, 092703 (2010)
Article history
Received:
February 15 2010
Accepted:
July 16 2010
Citation
Yang Zhijian; Finite-dimensional attractors for the Kirchhoff models. J. Math. Phys. 1 September 2010; 51 (9): 092703. https://doi.org/10.1063/1.3477939
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