TITLE:
The Inertial Manifold for Class Kirchhoff-Type Equations with Strongly Damped Terms and Source Terms
AUTHORS:
Guoguang Lin, Xiangshuang Xia
KEYWORDS:
Inertial Manifold, Hadamard’s Graph Transformation Method, Lipschitz Continuous, Spectral Gap Condition
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.6,
June
29,
2018
ABSTRACT: In this paper, we study the inertial manifolds for a class of the Kirchhoff-type
equations with strongly damped terms and source terms. The inertial manifold
is a finite dimensional invariant smooth manifold that contains the global
attractor, attracting the solution orbits by the exponential rate. Under appropriate
assumptions, we firstly exert the Hadamard’s graph transformation
method to structure a graph norm of a Lipschitz continuous function, and
then we prove the existence of the inertial manifold by showing that the spectral
gap condition is true.