Abstract

This paper considers the long-time behavior for a system of coupled wave equations of higher-order Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of the inertial manifold while such equations satisfy the spectral interval condition.

Highlights

  • License (CC BY 4.0).http://creativecommons.org/licenses/by/4.0/ The concept of inertial manifold proposed by C

  • It is closely related to infinite and finite dimensional dynamic systems, that is, the existence of inertial manifold in infinite-dimensional dynamical system is reduced to the existence of inertial manifold in finite-dimensional dynamical system

  • When the system demonstrated by restriction to the inertial manifold, it reduces to finite-dimensional ordinary differential equation, at this point, the system is called the inertial system

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Summary

Introduction

When the system demonstrated by restriction to the inertial manifold, it reduces to finite-dimensional ordinary differential equation, at this point, the system is called the inertial system As in this following, the existence of such manifold relies on a spectral gap condition that turns out to be very restrictive for the applications. Wu Jingzhu and Lin Guoguang introduced the graph transformation method in [5] to obtain the existence of inertial manifold for a two-dimensional damped Boussinesq equation with α > 2 , utt − α∆ut − ∆u + u2k+1 = f ( x, y). In this paper, basing on previous studies, the existence of the inertial manifold for nonlinear Kirchhoff type equations with higher-order strong damping is considered by using the Hadamard graph transformation method.

Preliminaries
Inertial Manifold
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