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.