Author(s)

Guoguang Lin^*, Xiaomei Liu

Department of Mathematics, Yunnan University, Kunming, China.

In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space E₀ to E_k, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.

A Family of the Exponential Attractors, Inertial Fractal Set, Squeezing Property, Spectral Gap Condition, A Family of the Inertial Manifolds

Lin, G. and Liu, X. (2022) The Family of Exponential Attractors and Inertial Manifolds for a Generalized Nonlinear Kirchhoff Equations. Journal of Applied Mathematics and Physics, 10, 172-189. doi: 10.4236/jamp.2022.101013.