Abstract
The existence of inertial manifolds for higher-order Kirchhoff type equations with strong damping terms is studied. The Hadamard graph norm conversion method is used for obtaining the existence of inertial manifolds for this kind of equations under certain spectral intervals.
Highlights
In the study of the long-term dynamic behavior of infinite dimensional dynamical systems, the inertial manifold occupies an important position
The Hadamard graph norm conversion method is used for obtaining the existence of inertial manifolds for this kind of equations under certain spectral intervals
It is a finite dimensional invariant Lipschitz manifold and attracts all solution orbitals with exponential rate in the phase space of the system [1,2,3]. It plays an important role in both finite dimensional dynamical systems and infinite dimensional dynamical systems.Because it occupies an important position, many scholars have studied the existence and attraction of inertial manifolds, the finite-dimensional properties, and the related problems of approximate inertial manifolds and delay
Summary
In the study of the long-term dynamic behavior of infinite dimensional dynamical systems, the inertial manifold occupies an important position It is a finite dimensional invariant Lipschitz manifold and attracts all solution orbitals with exponential rate in the phase space of the system [1,2,3]. Zhicheng Zhang and Guoguang Lin [5] study the following fourth order strongly damped time-delay wave equations: utt − ε∆ut − ∆u + ∆2u = f (ut), t > 0, u0(Θ) = u0(Θ), Θ ∈ [−r, 0], ∂t|t=0 = u. This paper study the initial boundary value problems of the following Kirchhoff type equations: utt + (1 + Ω |Dmu|pdx)r(−∆)mu + ∆2mu + β(−∆)mut =. The assumptions about the rigid term will be given late
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