Author(s)

Yunlong Gao^*, Yuting Sun, Guoguang Lin

Department of Mathematics, Yunnan University, Kunming, China.

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.

Nonlinear Higher-Order Kirchhoff Type Equation, The Existence and Uniqueness, The Global Attractors, Hausdorff Dimensions, Fractal Dimensions

Gao, Y. , Sun, Y. and Lin, G. (2016) The Global Attractors and Their Hausdorff and Fractal Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation with Strong Linear Damping. International Journal of Modern Nonlinear Theory and Application, 5, 185-202. doi: 10.4236/ijmnta.2016.54018.