TITLE:
A Family of Exponential Attractors and Inertial Manifolds for a Class of Higher Order Kirchhoff Equations
AUTHORS:
Guoguang Lin, Yingguo Wang
KEYWORDS:
Kirchhoff Equation, Lipschitz Property, Squeezing Property, a Family of the Exponential Attractors, a Family of Inertial Manifolds
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.3,
March
25,
2022
ABSTRACT: 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.