The Family of Global Attractors of Coupled Kirchhoff Equations  

作　　者：Guoguang Lin Fumei Chen Guoguang Lin;Fumei Chen(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5期1651-1677,共27页应用数学与应用物理（英文）

摘　　要：In this paper, we study the initial boundary value problem of coupled generalized Kirchhoff equations. Firstly, the rigid term and nonlinear term of Kirchhoff equation are assumed appropriately to obtain the prior estimates of the equation in E₀ and E_k space, and then the existence and uniqueness of solution is verified by Galerkin’s method. Then, the solution semigroup S(t) is defined, and the bounded absorptive set B_k is obtained on the basis of prior estimation. Through using Rellich-Kondrachov compact embedding theorem, it is proved that the solution semigroup S(t) has the family of the global attractors A_k in space E_k. Finally, by linearizing the equation, it is proved that the solution semigroup S(t) is Frechet differentiable on E_k, and the family of global attractors A_k have finite Hausdroff dimension and Fractal dimension.In this paper, we study the initial boundary value problem of coupled generalized Kirchhoff equations. Firstly, the rigid term and nonlinear term of Kirchhoff equation are assumed appropriately to obtain the prior estimates of the equation in E₀ and E_k space, and then the existence and uniqueness of solution is verified by Galerkin’s method. Then, the solution semigroup S(t) is defined, and the bounded absorptive set B_k is obtained on the basis of prior estimation. Through using Rellich-Kondrachov compact embedding theorem, it is proved that the solution semigroup S(t) has the family of the global attractors A_k in space E_k. Finally, by linearizing the equation, it is proved that the solution semigroup S(t) is Frechet differentiable on E_k, and the family of global attractors A_k have finite Hausdroff dimension and Fractal dimension.

关 键 词：Kirchhoff Equation Prior Estimation Existence and Uniqueness of Solutions The Family of Global Attractors Dimension Estimation 

分 类 号：O17[理学—数学]