Author(s)

Guoguang Lin, Yingguo Wang

Department of Mathematics, Yunnan University, Kunming, China.

In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup associated with the initial boundary value problem are proved, and the existence of a family of exponential attractors is obtained. Then, by constructing the corresponding graph norm, the condition of a spectral interval is established when N is sufficiently large. Finally, the existence of the family of inertial manifolds is obtained.

Kirchhoff Equation, Lipschitz Property, Squeezing Property, a Family of the Exponential Attractors, a Family of Inertial Manifolds

Lin, G. and Wang, Y. (2022) A Family of Exponential Attractors and Inertial Manifolds for a Class of Higher Order Kirchhoff Equations. Journal of Applied Mathematics and Physics, 10, 900-914. doi: 10.4236/jamp.2022.103062.