TITLE:
The Global Attractors and Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation with Strong Damping
AUTHORS:
Guoguang Lin, Yalan Yang
KEYWORDS:
Nonlinear Higher-Order Kirchhoff Type Equation, The Priori Estimates, The Galerkin’s Method, The Global Attractors, Dimension Estimation
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.9 No.4,
November
4,
2020
ABSTRACT: The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.