%0 Journal Article %T Global Attractors and Their Dimension Estimates for a Class of Generalized Kirchhoff Equations %A Guoguang Lin %A Lujiao Yang %J Advances in Pure Mathematics %P 317-333 %@ 2160-0384 %D 2021 %I Scientific Research Publishing %R 10.4236/apm.2021.114020 %X 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. %K Generalized Kirchhoff Equation %K The Existence and Uniqueness of Solution %K A Family of the Global Attractor %K Dimension Estimation %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=108646