TITLE:
The Family of Global Attractors for Kirchhoff-Type Coupled Equations
AUTHORS:
Guoguang Lin, Jiaying Zhou
KEYWORDS:
Kirchhoff Equation, the Existence and Uniqueness of Global Solution, the Family of Global Attractors, Hausdorff Dimension and Fractal Dimension of Global Attractor
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.6,
June
30,
2022
ABSTRACT: This paper mainly studies the initial value problems of Kirchhoff-type coupled equations. Firstly, by giving the hypothesis of Kirchhoff stress term , the Galerkin’s method obtains the existence uniqueness of the overall solution of the above problem by using a priori estimates in the spaces of E0 and Ek, and secondly, it proves that there is a family of global attractors for the above problem, and finally estimates the Hausdorff dimension and the Fractal dimension of the family of global attractors.