Open AccessThe global attractors and their Hausdorff and fractal dimensions estimation for the higher-order nonlinear Kirchhoff-type equation*
Author(s) -
Ling Chen,
Wei Wang,
Gao Lin
Publication year - 2016
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v12i9.133
Subject(s) - mathematics , attractor , uniqueness , hausdorff dimension , fractal , fractal dimension , nonlinear system , hausdorff space , mathematical analysis , type (biology) , order (exchange) , a priori and a posteriori , dimension (graph theory) , a priori estimate , pure mathematics , physics , ecology , philosophy , finance , epistemology , quantum mechanics , economics , biology
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  ï€ ï„ u  ï¦ ï D u ï ( ) ( ) ( )mï€ ï„ 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.