Estimate on the Dimension of Global Attractor for Nonlinear Dissipative Kirchhoff Equation

Zhang ZY; Liu ZH; Miao XJ

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Estimate on the Dimension of Global Attractor for Nonlinear Dissipative Kirchhoff Equation

机译：非线性耗散Kirchhoff方程整体吸引子的维数估计。

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摘要

In this paper,we estimate the dimension of the global attractor for nonlinear dissipative Kirchhoff equation in Hilbert spaces H (0) (1) xL (2)(Omega) and D(A)xH (0) (1) (Omega). Using rescaling technology and linear variation method, we obtain the upper bound for its Hausdorff and fractal dimensions.

机译：在本文中，我们估计了希尔伯特空间H（0）（1）xL（2）（Ω）和D（A）xH（0）（1）（Ω）中非线性耗散Kirchhoff方程的整体吸引子的维数。使用重标度技术和线性变化方法，我们获得了其Hausdorff和分形维数的上限。

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《Acta Applicandae Mathematicae: An International Journal on Applying Mathematics and Mathematical Applications》 |2010年第1期|共12页
作者
Zhang ZY; Liu ZH; Miao XJ;
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正文语种 eng
中图分类应用数学;
关键词
Kirchhoff equation; Rescaling; Global attractor; Lyapunov exponents; Hausdorff dimensions; Fractal dimensions;

机译：Kirchhoff方程;重新定标;整体吸引子;Lyapunov指数;Hausdorff维度;分形维度;

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1. Estimate on the Dimension of Global Attractor for Nonlinear Dissipative Kirchhoff Equation [J] . Zhang ZY, Liu ZH, Miao XJ Acta Applicandae Mathematicae: An International Journal on Applying Mathematics and Mathematical Applications . 2010,第1期

机译：非线性耗散Kirchhoff方程整体吸引子的维数估计。
2. The Estimates of the Upper Bounds of Hausdorff Dimensions for the Global Attractor for a Class of Nonlinear Coupled Kirchhoff-Type Equations [J] . Guoguang Lin, Ming Zhang Advances in Pure Mathematics . 2018,第1期

机译：一类非线性耦合Kirchhoff型方程整体吸引子Hausdorff维数上限的估计。
3. Estimate on the Dimension of Global Attractor for Nonlinear Higher-Order Coupled Kirchhoff Type Equations [J] . Guoguang Lin, Lingjuan Hu Advances in Pure Mathematics . 2018,第1期

机译：非线性高阶耦合Kirchhoff型方程整体吸引子的维数估计。
4. Existence of global attractor of equations of Kirchhoff type [C] . Li Bao-ping International Conference on Natural Computation;International Conference on Fuzzy Systems and Knowledge Discovery . 2015

机译：Kirchhoff型方程整体吸引子的存在
5. Nonchaotic features of the global attractor of dissipative partial differential equations. [D] . Kukavica, Igor. 1993

机译：耗散偏微分方程整体吸引子的非混沌特征。
6. Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation [O] . Daewook Kim, Dojin Kim, Keum-Shik Hong, -1

机译：具有非线性耗散的Kirchhoff型波动方程的整体存在和能量衰减率
7. The Estimates of the Upper Bounds of Hausdorff Dimensions for the Global Attractor for a Class of Nonlinear Coupled Kirchhoff-Type Equations [O] . Guoguang Lin, Ming Zhang 2018

机译：对一类非线性耦合Kirchhoff型方程的全局吸引子的Hausdorff尺寸上限的估计

Estimate on the Dimension of Global Attractor for Nonlinear Dissipative Kirchhoff Equation

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