Gao, Y.L., Sun, Y.T. and Lin, G.G. (2016) The Global Attractors and Their Hausdorff and Fractal Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation with Strong Linear Damping. International Journal of Modern Nonlinear Theory and Application, 5, 185-202.

has been cited by the following article:

• 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.