scholarly journals Global Attractor of Two-Dimensional Strong Damping KDV Equation and Its Dimension Estimation

2014 ◽  
Vol 05 (01) ◽  
pp. 7-15 ◽  
Author(s):  
Cheng Zhang ◽  
Guoguang Lin
Keyword(s):  
Global Attractor ◽  
Kdv Equation ◽  
Two Dimensional ◽  
Dimension Estimation ◽  
Strong Damping

scholarly journals Existence of Global Attractors for the Nonlinear Plate Equation with Memory Term

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Lifang Niu ◽  
Jianwen Zhang
Keyword(s):  
Rectangular Plate ◽  
Global Attractor ◽  
Exponential Decay ◽  
Global Attractors ◽  
Memory Term ◽  
Two Dimensional ◽  
Plate Equation ◽  
Memory Kernel ◽  
Nonlinear Plate ◽  
With Memory

A two-dimensional nonlinear plate equation is revisited, which arises from the model of the viscoelastic thin rectangular plate with four edges supported. We establish that the system is exponentially decayed if the memory kernel satisfies the condition of the exponential decay. Furthermore, we show the existence of the global attractor by verifying the condition (C).

scholarly journals Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Zai-yun Zhang ◽  
Zhen-hai Liu
Keyword(s):  
Global Attractor ◽  
Decomposition Method ◽  
Kdv Equation ◽  
Sobolev Embedding ◽  
Initial Condition

We discuss global attractor for the generalized dissipative KDV equation with nonlinearity under the initial conditionu(x,0)=u0(x). We prove existence of a global attractor in spaceH2(Ω), by using decomposition method with cut-off function andKuratowskiα-measure in order to overcome the noncompactness of the classical Sobolev embedding.

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