TITLE:
A Family of the Global Attractor for Higher Order Nonlinear Kirchhoff Equation
AUTHORS:
Guoguang Lin, Yingguo Wang
KEYWORDS:
Kirchhoff-Type Equations, Prior Estimation, Galerkin’s Method, The Family of Global Attractor, Hausdorff Dimension, Fractal Dimension
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.11 No.6,
June
30,
2021
ABSTRACT: In this paper,we study the wellness and long time dynamic behavior of the solution of the initial boundary value problem for a class of higher order Kirchhoff equations with strong damping terms. We will properly assume the stress term M(s) and nonlinear term g(ut). First, we can prove the existence and uniqueness of the solution of the equation via a prior estimate and Galerkin’s method, then the existence of the family of global attractor is obtained. At last, we can obtain that the Hausdorff dimension and Fractal dimension of the family of global attractor are finite.