TITLE:
The Family of Exponential Attractors and Inertial Manifolds for a Generalized Nonlinear Kirchhoff Equations
AUTHORS:
Guoguang Lin, Xiaomei Liu
KEYWORDS:
A Family of the Exponential Attractors, Inertial Fractal Set, Squeezing Property, Spectral Gap Condition, A Family of the Inertial Manifolds
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.1,
January
24,
2022
ABSTRACT: 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 Ek, 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.