Chen, L., Wang, W. and Lin, G. (2016) The Global Attractors and Their Hausdorff and Fractal Dimensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type Equation. Journal of Advances in Mathematics, 12, 6608-6621.
https://doi.org/10.24297/jam.v12i9.133

has been cited by the following article:

• TITLE: A Family of Global Attractors for the Generalized Kirchhoff-Beam Equations

  AUTHORS: Guoguang Lin, Boshi Chen

  KEYWORDS: Beam-Kirchhoff Equation, Galerkin’s Method, Family of Global Attractors, Housdorff Dimension, Fractal Dimension

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.7, July 25, 2023

  ABSTRACT: In this paper, we discuss the existence and uniqueness of global solutions, the existence of the family of global attractors and its dimension estimation for generalized Beam-Kirchhoff equation under initial conditions and boundary conditions, using the previous research results for reference. Firstly, the existence of bounded absorption set is proved by using a prior estimation, then the existence and uniqueness of the global solution of the problem is proved by using the classical Galerkin’s method. Finally, Housdorff dimension and fractal dimension of the family of global attractors are estimated by linear variational method and generalized Sobolev-Lieb-Thirring inequality.