Author(s)

Guoguang Lin, Boshi Chen

Department of Mathematics, Yunnan University, Kunming, China.

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.

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

Lin, G. and Chen, B. (2023) A Family of Global Attractors for the Generalized Kirchhoff-Beam Equations. Journal of Applied Mathematics and Physics, 11, 1945-1963. doi: 10.4236/jamp.2023.117126.