Finite-dimensional attractors for the Kirchhoff models

被引:16
|
作者
Yang Zhijian [1 ]
机构
[1] Zhengzhou Univ, Dept Chem, Zhengzhou 450052, Peoples R China
关键词
elastoplasticity; fractals; initial value problems; plastic flow; turbulence; SEMILINEAR WAVE-EQUATION; GLOBAL ATTRACTORS; LONGTIME BEHAVIOR; TIME BEHAVIOR; EXISTENCE; NONEXISTENCE; UNIQUENESS;
D O I
10.1063/1.3477939
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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 u(tt)-div{vertical bar del u vertical bar(m-1)del u}-Delta(2)u+h(u(t))+g(u)=f(x). By using the method of e-trajectories and the operator technique, it proves that under subcritical case, 1 <= m < N+2/(N-2)(+), 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. (C) 2010 American Institute of Physics. [doi:10.1063/1.3477939]
引用
收藏
页数:25
相关论文
共 50 条