The global attractors and their Hausdorff and fractal dimensions estimation for the higher-order nonlinear Kirchhoff-type equation*

Abstract

We investigate the global well-posedness and the longtime dynamics of solutions for the higher-order Kirchhoff-typeequation with nonlinear strongly dissipation:2( ) ( )m mt t tu    u    D u  ( ) ( ) ( )m  u  g u  f x . Under of the properassume, the main results are that existence and uniqueness of the solution is proved by using priori estimate and Galerkinmethod, the existence of the global attractor with finite-dimension, and estimation Hausdorff and fractal dimensions of theglobal attractor.