The Family of Global Attractors for Kirchhoff-Type Coupled Equations  

作　　者：Guoguang Lin Jiaying Zhou Guoguang Lin;Jiaying Zhou(Department of Mathematics, Yunnan University, Kunming, China)

机构地区：[1]Department of Mathematics, Yunnan University, Kunming, China

出　　处：《Journal of Applied Mathematics and Physics》2022年第6期2040-2060,共21页应用数学与应用物理（英文）

摘　　要：This paper mainly studies the initial value problems of Kirchhoff-type coupled equations. Firstly, by giving the hypothesis of Kirchhoff stress term , the Galerkin’s method obtains the existence uniqueness of the overall solution of the above problem by using a priori estimates in the spaces of E₀ and E_k, and secondly, it proves that there is a family of global attractors for the above problem, and finally estimates the Hausdorff dimension and the Fractal dimension of the family of global attractors.This paper mainly studies the initial value problems of Kirchhoff-type coupled equations. Firstly, by giving the hypothesis of Kirchhoff stress term , the Galerkin’s method obtains the existence uniqueness of the overall solution of the above problem by using a priori estimates in the spaces of E₀ and E_k, and secondly, it proves that there is a family of global attractors for the above problem, and finally estimates the Hausdorff dimension and the Fractal dimension of the family of global attractors.

关 键 词：Kirchhoff Equation the Existence and Uniqueness of Global Solution the Family of Global Attractors Hausdorff Dimension and Fractal Dimension of Global Attractor 

分 类 号：O17[理学—数学]