The Global Attractors and Their Hausdorff and Fractal Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation with Strong Linear Damping  

作　　者：Yunlong Gao Yuting Sun Guoguang Lin Yunlong Gao;Yuting Sun;Guoguang Lin(Department of Mathematics, Yunnan University, Kunming, China)

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

出　　处：《International Journal of Modern Nonlinear Theory and Application》2016年第4期185-202,共18页现代非线性理论与应用（英文）

摘　　要：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.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.

关 键 词：Nonlinear Higher-Order Kirchhoff Type Equation The Existence and Uniqueness The Global Attractors Hausdorff Dimensions Fractal Dimensions 

分 类 号：O17[理学—数学]