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
Summary
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.
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