Article citationsMore>>

Ai, C.F, Zhu, H.X. and Lin, G.G. (2016) Approximate Inertial Manifold for a Class of the Kirchhoff Wave Equations with Nonlinear Strongly Damped Terms. International Journal of Modern Nonlinear Theory and Application, 5, 218-234.
https://doi.org/10.4236/ijmnta.2016.54020

has been cited by the following article:

• TITLE: A Family of Inertial Manifolds for a Class of Asymmetrically Coupled Generalized Higher-Order Kirchhoff Equations

  AUTHORS: Guoguang Lin, Min Shao

  KEYWORDS: Inertial Manifold, Hadamard’s Graph Transformation Method, Lipschitz Continuous, Spectral Gap Condition

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.12 No.7, July 15, 2022

  ABSTRACT: In this paper, we study the inertial manifolds for a class of asymmetrically coupled generalized Higher-order Kirchhoff equations. Under appropriate assumptions, we firstly exist Hadamard’s graph transformation method to structure a graph norm of a Lipschitz continuous function, then we prove the existence of a family of inertial manifolds by showing that the spectral gap condition is true.