TITLE:
The Family of Global Attractors of Coupled Kirchhoff Equations
AUTHORS:
Guoguang Lin, Fumei Chen
KEYWORDS:
Kirchhoff Equation, Prior Estimation, Existence and Uniqueness of Solutions, The Family of Global Attractors, Dimension Estimation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.5,
May
26,
2022
ABSTRACT: In this paper, we study the initial boundary value problem of coupled generalized Kirchhoff equations. Firstly, the rigid term and nonlinear term of Kirchhoff equation are assumed appropriately to obtain the prior estimates of the equation in E0 and Ek space, and then the existence and uniqueness of solution is verified by Galerkin’s method. Then, the solution semigroup S(t) is defined, and the bounded absorptive set Bk is obtained on the basis of prior estimation. Through using Rellich-Kondrachov compact embedding theorem, it is proved that the solution semigroup S(t) has the family of the global attractors Ak in space Ek. Finally, by linearizing the equation, it is proved that the solution semigroup S(t) is Frechet differentiable on Ek, and the family of global attractors Ak have finite Hausdroff dimension and Fractal dimension.