Open AccessThe global attractors and exponential attractors for a class of nonlinear damping Kirchhoff equation
Author(s) -
Huixian Zhu,
Chengfei Ai,
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.v12i10.115
Subject(s) - attractor , mathematics , uniqueness , mathematical analysis , galerkin method , nonlinear system , a priori and a posteriori , class (philosophy) , exponential function , boundary value problem , a priori estimate , physics , philosophy , epistemology , quantum mechanics , artificial intelligence , computer science
This paper consider the long time behavior of a class of nonlinear damped Kirchhoff equation    2 tt 1 t t u u u u u f x ï² ï€«ï¡ ï€ï§ï„ ï€ ï¡ ï€«ï¢ ïƒ‘ ï„ ï€½ . Study the attractor problem with initial boundary value conditions, then using priori estimate and the Galerkin method prove existence and uniqueness of solution, we obtain to the existence of the global attractors. The squeezing property of the nonlinear semi-group associated with this equation and the existence of exponential attractors are also proved.