The global attractors and their Hausdorff and fractal dimensions estimation for the higher-order nonlinear Kirchhoff-type equation* - Chen, Ling; Wang, Wei; Lin, Guoguang (JOURNAL OF ADVANCES IN MATHEMATICS, 2016)
We investigate the global well-posedness and the longtime dynamics of solutions for the higher-order Kirchhoff-type equation with nonlinear strongly dissipation: 2 ( ) ( ) m m t t t u ï€« ï€ ï„ u ï€« ï¦ ï D u ï ( ) ( ) ( ) m ï€ ï„ u ï€« g u ï€½ f x . Under of the proper assume, the main results are that existence and uniqueness of the solution is proved by using priori estimate and Galerkin method, the existence of the global attractor with finite-dimension, and estimation Hausdorff and fractal dimensions of the global attractor.