Author(s)

Guoguang Lin, Lujiao Yang

Department of Mathematics, Yunnan University, Kunming, China.

In this paper, we studied the long-time properties of solutions of generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for the nonlinear source term g (u) and Kirchhoff stress term M (s) in the equation, and the existence and uniqueness of the solution are proved by using uniform prior estimates of time and Galerkin’s finite element method. Then, abounded absorption set B_0k is obtained by prior estimation, and the Rellich-kondrachov’s compact embedding theorem is used to prove that the solution semigroup S (t) generated by the equation has a family of the global attractor A_k in the phase space . Finally, linearize the equation and verify that the semigroups are Frechet diifferentiable on E_k. Then, the upper boundary estimation of the Hausdorff dimension and Fractal dimension of a family of the global attractor A_k was obtained.

Generalized Kirchhoff Equation, The Existence and Uniqueness of Solution, A Family of the Global Attractor, Dimension Estimation

Lin, G. and Yang, L. (2021) Global Attractors and Their Dimension Estimates for a Class of Generalized Kirchhoff Equations. Advances in Pure Mathematics, 11, 317-333. doi: 10.4236/apm.2021.114020.