《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (12): 1-11.

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### 一类高阶非线性Kirchhoff方程吸引子族及其维数

1. 云南大学数学与统计学院, 云南 昆明 650500
• 发布日期:2019-12-11
• 作者简介:林国广(1964— ),男,博士,教授,研究方向为非线性偏微分方程. E-mail:gglin@ynu.edu.cn
• 基金资助:
国家自然科学基金资助项目(11561076)

### Attractor family and dimension for a class of high-order nonlinear Kirchhoff equations

LIN Guo-guang, LI Zhuo-xi

1. School of Mathematics and Statistics, Yunnan University, Kunming 650500, Yunnan, China
• Published:2019-12-11

Abstract: The initial boundary value problem for a class of high-order Kirchhoff equations with nonlinear nonlocal source terms and strong damping terms is studied. For the nonlinear nonlocal source term and the Kirchhoff stress term, the existence and uniqueness of the global solution of the equation are firstly proved by Galerkin finite element method and a prior estimate. Then the bounded absorption set is obtained by a prior estimate, so the global attractor family of high-order nonlinear Kirchhoff equation is obtained. By linearizing the equation and proving the Frechet differentiable of the solution semigroup, it further proves the decay of the volume element of the linearization problem. Finally, the Hausdorff dimension and Fractal dimension of the global attractor family are proved to be finite.

• O175.29
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