具有强线性阻尼的高阶非线性kirchhoff型方程的全局吸引子及其Hausdorff和分形维数估计

Yunlong Gao, Yuting Sun, Guoguang Lin
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引用次数: 5

摘要

本文研究了一类强阻尼高阶Kirchhoff型方程初边值问题解的长时性。首先,我们利用先验估计和伽辽金方法证明了解的存在唯一性。然后,我们得到了全局吸引子的存在性。最后,给出了全局吸引子的Hausdorff维数和分形维数上界的估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Global Attractors and Their Hausdorff and Fractal Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation with Strong Linear Damping
In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
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